London Hotels (May 30 - June 4)

Premier Inns don't have local charm; they are what I call "business hotels", and the rooms tend to look pretty much alike no matter which one you stay in. But I've always thought the beds were really comfortable, and I believe others agree with me. There are lots of PIs in London, and it's normally not a problem to find a room for less than your target rate. I've taken a quick look, and it looks as if availability is good and rates are reasonable for your time period. Since you've easily got the budget for one of the regular Premier Inns, I'd skip the "Hub" hotels; their rooms are reportedly really cramped for two people.

I've stayed at both the County Hall and the Holborn Premier Inns and been satisfied with them, but you should select a hotel whose location aligns with your sightseeing plans.

The Premier Inn website tends to be flakey, sometimes shifting the arrival date by one day as you go through the reservation process. Two possible solutions to try: Use PI's app or book on your phone or tablet after changing your location to match London's time zone. There's a good chance one of those techniques will avoid the problem many of us have encountered.

I should warn you that Premier Inns give very good value for money, but one way they do that is by trimming front desk staff. If you prefer a place where you'll get a lot of front-desk support, Premier Inns are not the best option for you.

Premier Inn beds are great. This is from their website:

Our Premier Inn Mattress 2.0 made exclusively with Silentnight is a luxurious medium firm mattress with breathable materials to keep you cooler, Geltex® foam to give you extra comfort and 1000 pocket zoned spring system to support you while you sleep.

Which mattress is best for back pain?
The best mattresses for back pain are ones that support your spine while sleeping. Pocket sprung mattresses are among the best beds for back pain.

Is a hard bed good for a bad back?
If you have a bad back, your bed should be strong enough to support your body while you sleep, but not too hard that your back becomes rigid. A bed with a medium firmness should do the trick.*

I stayed at Hotel 63 while in London. It was recommended to me by someone on Forum. Very small B&B in an excellent location (right across from Kensington Gardens)

I stayed in the "cheapest" room for one and could not recommend my room but they had some very pretty rooms that i know were more expensive. I do not know if the cost is within your budget. If you had any interest, you might contact them and ask about mattress.

They were. a nice group

I think your safest option is a reliable chain hotel, not a local Band B. Sheratons are known for their good mattresses, but their Park Lane location in London is above your price point. On the other hand, as Frank II states, the Premier Inns are proud of their mattresses. Here is the actual link:

https://www.premierinn.com/gb/en/sleep/our-bed.html

With locations all over London, you are spoiled for choice. County Hall is an excellent location, right across the Westminster Bridge from Westminster Abbey and “Big Ben”. But there are other good locations as well.

I agree with the recommendation for Premier Inns. I just finished a 5 night stay there, and I have never slept better. Their beds really are comfortable. In fact, I like the hotel I'm staying in now in Cornwall, but I miss the PI bed. :-)

What hotels are recommended by Rick Steves tours?

I went on the Rick Steves City of London tour in December 2019. We stayed at the Washington Mayfair. Nice hotel in a good location.

We learned about Vancouver Studios in London on this forum & couldn't be happier with the location, hotel & our entire 5 night stay there. The cost for our 3/15/24 arrival was 221 pounds & that translated to roughly 278 US dollars, I believe. Unsure about the prices or availability going into May or if you have booked something yet.
The location couldn't have been more convenient with 2 tube stations close by & the bus as well. Steps from Portobello Road & their market, Notting Hill & Kensington Gardens/Hyde Park. It was so quiet, well appointed with kitchenette that we did not use & the bed was fabulous!
There is a lovely garden out back which was nice to sit out in when we had the occasional dry minute.
The front desk was staffed round the clock. In my mind when I hear folks say they don't love London, I imagine they did not stay in an area as perfect as this area... I would stay in this area anytime that I visit London again.