Having drunkenly passed out in the standard cheapo room at the Union Jack club many a times after a night out in London, I would advise you to not have too high expectations. Single (and not a North American single) squeaky bed, small dresser, kettle and instant coffee/tea bags. Shared bath down a hall, and if you are a lucky a 2'x4' window with a view of the building opposite.
As stated, this is a brief description of the cheapest room type, which at the time was something like 34GBP a night. You can get ensuites for quite a bit more.
Having said all that, it is the cheapest hotel for miles, centrally located, and staggering distance to Soho/leicester square. And opposite waterloo station, so should you tire of the great smog, you can hop on a train to anywhere on the south coast of England.
Never stayed at the Victory Services club, but it is equally centrally located, although more in walking distance of piccadilly circus, Buck-P, and the west end/marble arch.
I would also recommend looking into hostels. There are a number of large scale, ''brand name'' hostels, which are very clean, safe, and lacking in eastern european butchers. For the same price as the above you can get a single room, shared bath, but with a younger, less military crowd.
