eeek, affordable hotels near soho? not the easiest...
unless you want to put some work in.
Check out the site www.londontown.com
. their hotel booking site is excellent, and very competitive. If you can put in some detective work, check out their "top secret deals" as well, because often you can figure out what hotel it is and you'll save even more money. I used to live in London, and the first time I went back for a visit I used this site and figured out that one of their "top secret" hotels was The Langham, a 4.5 star hotel about 50 yards north of Oxford Circus. It was a brilliant rate, something akin to US$130 a night.
If that's giving you no joy, also check out www.lastminute.com
, however the latter site will only show you hotels up to 21 days in advance.
Not sure how well you know London, so to be walking distance to Soho the areas you want to look in are Covent Garden, Leicester Square, Mayfair, Bloomsbury, Holborn, or simply West End.