Transportation from LHR to Paddington (Westminster Borough) London

Not sure where the price of €50 comes from, not just from not being in pounds sterling. You haven't said how old your kids are but if they are 15 or under they travel free, and adults start from £5.50 depending on how far in advance you are and what day of the week you are traveling, two other bits of info you haven't given.

Your public transport alternatives would be the Heathrow Connect, which depending on their age the children might have to pay a half fare on, or the Underground via Earls Court.

"Not sure where the price of €50 comes from, "

Assume the OP is looking at the Europe site rather than the UK one.

The OP wants to go to Paddington, and IMO the Piccadilly Line on the London Underground from Heathrow is an awkward option for that.

The Heathrow Express is the fastest and simplest way but not the least expensive.

There are other trains, which are not the Heathrow Express, which also run between Heathrow and Paddington. Those trains have been called the Heathrow Connect; they make some stops along the way but unless you're in a huge hot hurry to get to Paddington from LHR they are IMO just fine, and they cost less. IIRC they take more like 30 or 45 minutes instead of under 20 minutes, between LHR and Paddington.

Here's a new wrinkle about what used to be called the Heathrow Connect - those trains, that used to be part of the National Rail network, are now operated by Transport for London. TfL is London's public transport system. They have taken over this line serving Heathrow in preparation for opening of a new line of their service, the Elizabeth Line, sometime in the future. Details here: https://tfl.gov.uk/info-for/media/press-releases/2018/may/tfl-to-operate-heathrow-connect-services-ahead-of-elizabeth-line-opening

What that means is that now you can take the TfL train (formerly known as the Heathrow Connect) to Paddington, using an Oyster card. I don't know if you can buy a paper TfL ticket for it,. Anyway, most arriving tourists will probably get an Oyster card with enough on it to cover the train fare plus their public transport fares while in London. There are TfL staff at Heathrow who can help you with all that.

If you can get your whole family to Paddington for 50 Euro on the Express, that's fine.

For TfL Rail, aka Heathrow Rail, fka Heathrow Connect, you may want to explore the fares per person - here's a link: https://tfl.gov.uk/fares-and-payments/fares/single-fare-finder?intcmp=1660 . Choose "Heathrow Rail" and your arrival terminal number, and the destination as London Paddington Rail Station. The fares are different for children depending on their ages. Adults are at most £10.20 each with an Oyster card, children's fares depend on age, from free to a little over £5. Depending on their ages your kids' fares could bring down your family total to £30 or less.

Edited to add this: The TfL website has a great Journey Planner tool - https://tfl.gov.uk/plan-a-journey/ - but it's displaying an odd tic when it comes to the LHR-Paddington Rail Station trip. It only shows the Heathrow Express (which is NOT a TfL train) in the journey results. And it doesn't show TfL's own train from Heathrow. Yikes! Finally I discovered that you need to click on "Edit Preferences" in the search box area, which will open a screen where you can select, and de-select, methods of transport. I un-checked the box for "National Rail" and made sure the box for "TfL Rail" was checked. Then I ran the search again and the Heathrow Connect (now TfL Rail) trains came up. The results for the time I chose showed a 28 minute journey. Not bad, IMO.

(Here's what I figured out: The TfL Journey Planner defaults to 'fastest method by public transport' which if you include National Rail for that trip, is the Heathrow Express. If you're looking for TfL's own train as an option but you still want the fastest journey with that option, you have to change the preferences to rule out National Rail.)

This upcoming Thursday? If so, you are too late for any advance purchase discounts on the Heathrow Express. But if you will depart from Paddington back to Heathrow for your flight home (or elsewhere) after you time in London, you could look at a DuoSaver ticket, which is a round trip ticket for two adults on the Heathrow Express. You need to specify the first date (inbound to London) and the return date must be within 30 days.

Yes it wasn't altogether clear to me whether it was this coming Thursday or a generic one that the OP was arriving on. However, the duo saver won't be of any use from other questions which relate to an early departure time too early for the HEX - and a different part of London too. Although there maybe some other legs I guess.

Thanks for all the information everyone! I missed the 3-month pre-order window for the kids 11 - 15 yr old Oyster Cards. It looks like without those, the cost between the Rail Trains and the Heathrow Express is only about 10 GBP. I think we'll take the HEX to keep things simple since we would have been travelling for ~20 hours at that point. I appreciate your help. I look forward to visiting your beautiful city. Cheers!

For most people on a one-off visit the 11-15 Zip Oyster card struggles to pay off its issue fee. The Young Visitor Oyster card which discounts adult fares by 50% has no specific fee or administration hoops to jump through apart from getting the discount applied to a card.

Marco makes a good point.

If possible, find a TfL attendant at Heathrow when you buy your Oyster cards. He can set up a discount card for your 11 - 15 year old(s) right on the spot. That will work for the rest of your time in London.

But I also understand the fatigue after such a long trip, which means the simplest solution is often the best even if the cost is a bit more. There are times to count every penny, and there are times you have other priorities.

Just to be clear, I wasn't suggesting ditching the Express on arrival, but use of the Young Visitor Oyster option during the stay.

Marco and Hilda:

I'm sorry. I was reading and posting a little too fast this morning. I'd forgotten that Hilda's taking the Express vs. a train using Oyster cards from Heathrow. My bad!