Cheap London hotel

Most on here will recommend Premiere Inns.

Vancouver Studios is actually really nice and inexpensive for London. It’s not far from the Bayswater Tube.

If Premier Inns are too expensive for you, try Travelodge.

I stayed at a premier Inn just this fall in London and was happy with it. After paying for breakfast, it’s a lot more than the airport accommodation which includes breakfast. I’m going to have to give it some thought. Thank you.

As Frank mentioned, if you want something cheaper, try Travelodge. Here is a recent post where someone was looking for a very cheap London hotel, so you might find some options there. https://community.ricksteves.com/travel-forum/england/accommodation

One thing about Premier Inns - the earlier you book, the cheaper they are. So booking at the last minute will generally lead to higher prices.

What price range are you needing?
I stay at cheaper hotels. Last visit to London I stayed at http://www.cherrycourthotel.co.uk/ neat Victoria Station.
This year I will be staying at https://bb-london.co.uk/ in Fitzrovia. It was recommended on the forum.
Good luck finding somewhere that meets your needs.

The Fitzrovia B&B that Horsewoofie mentions is where we’ve stayed on all our last several London visits. For the surprisingly low price (for London), the location, Mike’s superior cooked-to-order breakfasts, and quality of the accommodations, it’s the best deal in London. There are only three rooms: a small, a medium, and one large (which is self-catering flat), but if you can get one of them, I can’t recommend them more highly.

Premier Inn and Travelodge pricing varies a lot depending on location. If you don't know the city too well it can be hard to sort out the wheat from the chaff in that process as some locations are not very convenient.
But the likes of Wimbledon and Croydon are often very good value. And both have very fast and frequent trains into Central London- Croydon especially and are within the TfL travel zones. Apart from the premium priced Piccadilly line to Heathrow the cost premium of travelling to outer zones (as opposed to the central London zones) is very minor.
Croydon also has a direct bus to Croydon on arrival- meaning you don't have to get there via Central London.

Another one which often works is the PI at Tottenham Hale. That is on the Victoria Line so travel to central London is very easy and quick (and also on the main line to Liverpool Street and Stratford for east London, such as Greenwich).

Where is it you want to be?

What do you consider cheap?

No offense to Stuart, but I wouldn't recommend Croydon or Tottenham Hale to visitors, even if they are cheap. I've only really been through Croydon on the way to other places, but I don't think it's in much doubt that it's somewhere with some of the most acute social problems in London.

Tottenham Hale is a bit rough. It would be fine if you're going straight from your hotel to the tube, but it's not that pleasant around there. Not dangerous as such, but just a bit meh. The main attraction to me is that it's the nearest retail park to me. Many big box retailers and drive thru fast food outlets are represented. I went to Pets At Home there just recently.

I lived in London and have visited probably 10 times since. I would never stay at the airport and travel in. You can easily get to and from the airport when you arrive and leave. Stay in the centre and enjoy your evenings in London.

My preference is Bloomsbury and the Imperial Group of hotels. The prices can be quite competitive - early booking rivals Premiere Inn.

We stayed at the Wimbledon Central Travelodge the night before the men's final last summer. Reasonable and close to train and bus options. Very quiet, too.

Does breakfast in the hotel really matter? There are many places to have a good breakfast or spring for breakfast one day and try something different other days.