where to stay in London

For roomy and a convenient location you might like a one bedroom apartment (with sofa bed in the living room) at Citadines' Trafalgar Square. It includes a mini-kitchen.

I haven't stayed here yet, but I am traveling with my adult son in May and we are planning to stay here. The location is about a 10 minute walk from the hotel I usually stay in, not far from the bus and not too far from the tube. The price was quite reasonable. The owner has been excellent with information and communication.
https://www.vrbo.com/439545ha?adultsCount=2&arrival=2022-05-02&departure=2022-05-08&unitId=1065757

In 2015 we stayed at what is now the Meliá London Kensington a block from the Gloucester tube stop. I think we stayed in room 101. Believe its suites might suit you. Upon entering there was a smaller room with a sofa bed and its own tv. Then you entered the main room. We stayed in one room while my daughter stayed in the other. We all shared the bathroom. It worked out well.

The Victoria neighborhood in London is where you’ll find budget lodging.

I’d go with adjoining rooms at a Premier Inn. Or 2 separate rooms.

Could also research the Vancouver Studio apartments on Princes Square.

There are numerous hotels with one bedroom suites. That means there is a living room--usually with a convertable sofa bed and a separate bedroom.

Or you could get two separate rooms each with it's own bathroo. For an adult son, is a connecting room really that necessary.

Or you could look at "serviced apartments." These are short term apartments run ike a hotel.

We have had good luck with Airbnb in London. We like Mayfair, Chelsea and West Kensington neighborhoods.