I stay in cheap London hotels quite a bit, basically the way I do it is:
-Search on
www.hotelscombined.com
-Filter for 3* and above, max £79, guest rating 6+, accomodation type hotel (i.e. excluding hostels etc)
-Look through the list to find hotels not too far from the city centre (their location filters suck) at a reasonable price
-Check nearby transport links - depends on where you need to get to/from obviously
-Make sure they are ensuite rooms etc
-Check Tripadvisor to make sure it isn't a complete dive
-Look for a seller offering at or very close to the lowest price with decent discount codes, e.g. Venere usually have a 15% discount code
For reference I have stayed both near Finsbury Park (quite a few times after going to football... I *think* from memory the best value in terms of quality relative to price was Pembury hotel at ~£52 but not sure) and Stratford (Epsilon hotel ~£48). I usually pay between £35-70 a night with varying quality - but I'm usually just wanting a single bed for the night, rather than a romantic night away.
Personally I tend to not worry too much about exact location so long as the nearby transport links work out well. London is so well connected that the best options is sometimes to stay further away but near a train station. I tend to end up staying in Bayswater area (between Hyde Park and Paddington) quite a lot because it seems to have a lot of reasonably priced hotels, it really doesn't take long to get elsewhere in London, a lot of them are literally like 2mins walk to Lancaster Gate / Queensway which is on Central line.