Transportation: London's Radisson Blu Edwardian Vanderbilt Hotel to LHR?

Use the TFL website. www.tfl.gov.uk

Piccadilly Line from Gloucester Road station to LHR terminal 5. 45 minutes.

You also have the option of buying a Heathrow Express ticket for that date now ( to save $’s ) and from Gloucester Road take a Circle Line train to Paddington. Exit and board The Heathrow Express to Terminal 5. 15 minute ride.

OR

Take the Circle line to Paddington and then take the Elizabeth Line to Terminal 5. About 45 minutes.

Love England and London is my favorite city on planet.

Do have cake and tea in the gorgeous V & A Museum. Great gift shop as well.
https://www.vam.ac.uk/articles/a-first-of-its-kind-history-of-the-refreshment-rooms

Enjoy the 14 day tour.

That’s our go hotel in London. Walk to the corner and from the Gloucester tube station Piccadilly Line (dark blue), it’s 45-55 minutes to Terminal 5. Ensure you get on the train that says terminal 5. If you get on the T2,3 train you’ll need to change trains at some point. The train runs frequently. No need to get your ticket in advance. If not using an Oyster Card, you simply need to tap your credit card. Use the same card to tap out at the airport. Easy.

Claudia did a great job providing all the options.

Take the tube.

The Heathrow Express is not a good option from where you are staying. It will not save you any time when you factor in waiting and connection time at Paddington. It will cost more. It is inconvenient as the change from the circle line to the train platform is a pain with luggage.

Short walk to Gloucester Road then 45 minutes on the Piccadilly line - no advance purchasing necessary or even possible. Don't even consider the HE or Elizabeth line

The entrance to the tube is diagonally across the street. Right next to Waitrose and the Gloucester Arcade. (I was there yesterday.)

Take the Piccadilly line to Heathrow. Make sure the train you get on is going to "Heathrow T2,3 & 5." The information board will have the destination of the next few trains. If you wait to get on the one going to T5 you won't have to change trains.

Do not, I repeat, do not use the Heathrow Express. It will be a waste of money, time and energy. You will have to change trains at Paddington and that includes walking. The same goes for the Elizabeth line.

I have taken the Piccadilly line to Heathrow more times than I can count. (I get on the next station from Gloucester Road....Earls Court.) In fact, I'll be going to Heathrow tomorrow.

No need to buy a ticket in advance. The fare doesn't change.

One hour from Gloucester Road to Heathrow on a bad day. Normally about 45 minutes.

All very helpful info - many thanks!

I'll just add that if you are using a contactless credit card to tap in and out of the tube both of you will need a card, you can't tap for 2 people on one card. The contactless card method is SO easy! You can also use ApplePay on your phones.

Also monitor what is going on at Heathrow up to the time you leave from home regarding the amount of time ahead of the flight that you will need to be there. Usually 3 hours ahead for an international flight is OK. Last summer airlines were recommending arriving 4 hours ahead because of slowdowns.

"Is it advisable to save time & money by purchasing tube/train tickets in advance?"

When you get to London, your guide for your RS Best of England tour will give everyone Oyster cards, and then take your group for a lesson on riding the tube.
You will walk from the Radisson (your tour hotel) across the street to the Gloucester Road tube station, the one Frank II told you about in his post.
You will "tap in" with your Oyster card, ride the tube, and when you're exiting, you will "tap out".
This will be your method of payment.
This will be a "practice run" for your tour group, with your guide.

On your day of departure to Heathrow, return to this same station, tap in with Oyster, ride the tube, tap out when you reach Heathrow T5.
This is one of the easiest journeys on the London tube.
Don't worry.....it will come naturally to you after your Rick Steves guide gives you the "riding the London tube" lesson.

On the morning of your farewell breakfast, and end of the tour, you may have several from your tour group making the same journey to Heathrow with you.

P.S. Do pay attention to what Pam said, about using the contactless card method or ApplePay.
The Oyster card is the way it has been done for years, but recently, many people are going to the methods Pam mentioned.
I assume the RS guide still gives out the Oyster card, but I would not be surprised if he instructs you to use one of the methods Pam mentioned instead.

Appreciate the helpful advice - thanks to all.