Discount fare on Heathrow

Perhaps go to the Heathrow Express website directly from your browser?

The link for advance purchase just tells you about the advance purchase. Click here and buy your tickets: https://www.heathrowexpress.com/en-GB#/

I clicked on the link. That's the one I have been trying all day. However, nothing relating to the discount fare appears

Use the link to price your journey. If it’s far enough out AND if there’s the cheap fares still available, the 5.5 pound each way offer will show up.

It’s possible that - even if you’re booking 90+ days in advance - the cheapest fares could be sold out.

Thank you for the information. It makes sense that it doesn't appear because it's sold out. That information should be posted.

If the cheapest rate is sold out, is the train still the best way to get to London, or is there a better way?

Are you staying near Paddington Station?

You can take Piccadilly Line train into London. It takes about 45 minutes. You will arrive at Paddington Station.

OR now you can take the new Elizabeth Line crossrail to Paddington.

You’ll need to research costs.

There has been another thread recently where it transpired that HEX have now changed the advance notice for their £5.50 fares to be 5 months, rather than the long standing 3 months.
The wording on the website has been altered to remove the 3 month wording and is now just vague, about being released in limited numbers, without stating that period. It is probably so as they can change the advance period at will without constantly updating the wording.

The period for advance HEX tickets has indeed moved from 3 to 5 months recently. There are other options to get into London including the new Elizabeth line.

London is a massive city. If you tell us where you are staying, we can give you options on the "best" way to get there.

It's possible that the Heathrow Express wouldn't be a good idea even if you could get the cheapest tickets.

We are staying at the Tower Hotel on St Katherine’s way. We will be there in mid May. Any suggestions regarding transportation from Heathrow to the hotel will be appreciated.
Thank you.
Honey

The easiest and cheapest route is to take the Piccadilly line from the airport and make a very simple cross platform change at either Barons Court or Hammersmith to the District line to Tower Hill from where the hotel is a very short walk. The change is literally feet.
There is a more expensive but slightly quicker route on the Elizabeth line to Whitechapel and change to the District line to Tower Hill. But that needs a more complicated change and a longer walk.
The Heathrow Express makes no sense whatever the ticket price.

I've had this issue with some merchant pay sites occasionally. Often trying with a different browser cured the problem.

As to OP's original question about not being able to click into the purchasing page(s):

I've had this issue with some merchant pay sites occasionally. Often
trying with a different browser cured the problem.

I have too. Just for reference, even if the advance bargain price is sold out, you can still proceed to the purchasing page(s) on the HEX website. Actually, that's where you find out if the £5.50 fare is available for the date(s) of your travel.

I had no trouble clicking through the HEX site today, so I think there was something about the OP's browser or connection that wasn't working. They should have been able to proceed to the booking/purchase pages where they could find out what fares are available for their dates.

As I pointed out above, as far as honeyth is concerned it's academic as s/he really should not take the Heathrow Express at any price for the journey she wants to do.

The HEX goes only to Paddington Station. Paddington Station is nowhere near where the OP wants to go.

The Tube or Elizabeth Line are a different matter.

You can take Piccadilly Line train into London. It takes about 45 minutes. You will arrive at Paddington Station.

The Piccadilly Line doesn’t go to Paddington Station.

As John New has pointed out above the route the OP wants is Piccadilly Line, changing to District Line (or the slightly more convoluted Elizabeth line route) to Tower Hill. The Piccadilly/District line route costs £5.50, the Elizabeth Line route £12.80 currently, both of which fares will have increased by 5.9% by the time she arrives. (the detailed new fare charts are not yet published so exact new fares are not currently available).
It is therefore a good job that there were technical issues with the HEX website as that would just have caused un-necessary difficulties and further expense for Holly.
Neither of those fares can be purchased in advance, but paid on the day using an Oyster Card or contactless, as per previous threads on this forum.

Thank you all for your replies. I am traveling with my daughter for her birthday and I want everything to go as well as possible. I guess the Piccadilly Line is the way to go. My concern is that we will arrive at Heathrow after traveling all night and we have luggage. Is it difficult to get to the train stations? Should we splurge and take a cab to avoid the hassle of making train connections; however, I heard that traffic from the airport is quite heavy. I am unsure which way will work out best.
Please advise.
Honey

No, the tube station is very clearly signposted from all terminals, and is all inside walking from the terminals. But follow the signs for the Underground, not for the HEX/Elizabeth line.
So no problems there.
A taxi won't be any faster, probably slower, as you are likely arriving in the morning peak but if you feel like a splurge for ease and convenience so be it. You will sit in a lot of traffic, but at least are comfortable
These days the tubes are quieter than in the past given the other options, and will gradually fill up as you go into London. Your change is in West London before they really fill up and Tower Hill is past the areas where everyone gets off.
How busy depends on what time you land and how long it takes to get into the Country.
The benefit of the Elizabeth line route is that they are very long trains so far more room and faster as fewer stops. The dis-benefit is the change.
Your choice!!

We're going to make this easy for you.

In which terminal do you arrive at Heathrow? If you don't know, what airline and from what city. Once we know this we can tell you how to find the underground. (Tube).

Once at the station, get on the Piccadilly line train. You'll have no trouble finding it. When you get to Hammersmith, get off the train, cross the small platform to the other side, and catch the District Line train. Get off at Tower Hill. From there it is an 8 minute walk. Look on Google Maps to find the routing.

If you are concerned about the walk, flag down a taxi when you exit at Tower Hill and it will take you the short distance to the hotel.

If this all seems like too much, you could arrange for a car service to take you from the airport to the hotel. I estimate it will run between 60 and 80 pounds. You'll know exactly when you book it.

Unless you want to go all the way across London in a cab and deal with whatever that brings (but (sleepy) daughter can ogle out the window all the way) the most comfortable and easiest has to be the Elizabeth Line all the way to Whitechapel, than an A-A stepfree https://content.tfl.gov.uk/step-free-tube-guide-map.pdf change to the District Line to the same place you would have been if you had changed at Barons Court. But 14 stops instead of 26, and on new track through new stations.

The Elizabeth line does have the benefit of being a bit quicker and slightly more comfortable (I think the differences are overstated), but the change at Whitechapel is much further and more difficult than the Piccadilly/District line change. And the Elizabeth line trains stay in stations quite a bit longer so the smaller number of stops is somewhat negated.
Some form of car or taxi will be way more expensive and almost certainly slower.

Let's confuse this poor poster even more with our arguments. She has stated that she is concerned about having to make this journey with luggage.

Here are your options:

1) Piccadilly line to Hammersmith or Barons Court. Switch to the District line and take it to Tower Hill. From Tower Hill it is less than a 10 minute walk to your hotel. I suggest looking at the routing on Google Maps if you plan to walk or if not, just hail a cab. (This is the least expensive way if you decide to walk.)

2) Elizabeth line to Whitechapel, switch to the District Line to Tower Hill. Continue as above. (This is slightly more expensive as the Elizabeth line has a small surcharge from Heathrow.)

3) Car Service from Heathrow. This may be slow due to traffic but it is door to door. You will know the price when you book but I estimate it to be around 60-80 GBP.

Bad ideas: Heathrow Express, National Express coach, taxi. (A taxi will run you well over 100 GBP.)

When you tell us which terminal you'll be using or airline you're traveling, we can tell you how to find the Underground station. It's very simple with plenty of signage.

by the way, when I use the word "taxi", I mean Black Cab, minicab, car service interchangeably.

The only difference is that a Black Cab, whilst being more expensive than a car service or minicab, for your birthday girl is the iconic shape, and big windows, high up. Hard to get more "London" than that except upstairs at the front of a double decker London bus.

Maybe if you do choose Black Cab you pay a little more and ask your driver to take the scenic route through Knightsbridge and past the Palace, past the Houses of Parliament and up Regent Street. Not too far out of the way, if she is awake and the driver is chatty.

How much luggage do you have? We've managed on the Tube and the trains with one rolling bag and one personal item that we're carrying on our body, such as a messenger bag or small backpack, per person. For me, wrestling with more luggage than this on public transportation would be too much after an international flight. (Actually, just traveling with more luggage than this would be too much for me.) So you might need to factor that in when making your decision. As Frank II said, car service is more expensive, but it is door to door.

Take another look. You have been given good information and several options.

From Frank II's post above:
"1) Piccadilly line to Hammersmith or Barons Court. Switch to the District line and take it to Tower Hill. From Tower Hill it is less than a 10 minute walk to your hotel."

Take the tube from Heathrow airport, after buying an Oyster card to use as payment.

I don't want to confuse you, so I will just say, if you don't want to fool with the tube, take a car service or taxi.

You could take Heathrow Express--what you originally asked about--and then just take a taxi from Paddington Station to your Tower Hill hotel.

You do not have to buy Heathrow Express tickets online. The representatives will be pestering you as you arrive at the airport to buy a Heathrow Express ticket. Easy to buy at Heathrow.

Or the circle line from Paddington to Tower Hill via Liverpool Street, that is clockwise.