London cheap eats?
This isn't really a "cheap" restaurant, but it is a reasonable alternative, and a bit different from the eastern/ethnic suggestions.
We like Lou Pescadou, french seafood, Brompton Rd, not far from the Earl's Court tube stop. They have very nice meals in a cozy atmosphere with decent service. We thought the food was really good and plan to return. Last year, we got a letter from them (don't remember signing a mailing list, but...) saying they had some prix fixe specials, I think before 7pm.
This place is not upscale, but neither is it a kebab house. You could dress casually and make it a splurge, even though it isn't all that expensive.
unfortunately, london just cant offer the diversity, quality and low, low prices for eating as so many american cities can...and that is, of course, because migration to the sceptered isle is so grudgingly granted.
and then, the prices. englands prices are usually a pound to a dollar; i.e, if it costs x dollars here, then x pounds is a good estimate of how much it costs in england. so you are already paying 50% (!) more, as it'll cost you about a buck and a half to buy a pound.
having said all that, i'd scout around notting hill for reasonably priced 'ethnic' food. you are bound to be steered to khans, which is unfortunate as its londons 6th street indian. not great food, huuuuge crowds. but cheap! (the kebabs aren't so bad, though). and talking about kebabs, the lucknowi kebab house has reasonably priced decent fare (i cant remember the address, unfortunately). the safest bet for subcontinental food is probably the veg. indians on drummond street (search chowhound.com by using 'london' and you'll get the posts).
the best deal for brit food is probably breakfast: bacon, eggs, toast and tea; you'll pay anywhere between 3 to 5 pounds. or muesli (shudder), if you are inclined that way. and dont miss high tea at any of the 'grand' hotels (try the savoy in the strand and see if you can get a seat overlooking the river); unfortunately, as londons getting so americanized, tea shops have given way to starbucks and the big hotels are about the only places where you'll get hot scones, clotted cream, preserves etc.
dont miss the food hall in harrods and dont miss fortnum and masons. theres plenty of delicious, moderately priced brit things you can get in these places, but see if you can score chicken/mutton/veg patties which are these fillings in a brioche-like looking pastry. you might try and check out the brit steak and kidney pies etc. here as well.
Try Cafe Naz on Brick Lane (I think). It's a Bangladeshi/Indian place with wonderful authentic food at a VERY good price (for London). Four of us ate for about $60 total (that's dollars, not pounds) including a couple of Indian beers. I was brought there by locals who dine there frequently.
It's in an "up-and-coming" area of town. So a cab might be better than the tube, but if you're on a budget -- live on the edge...
In response to Cathy's posting on cheap eats in London, there are plenty of decent places to get cheap food, although, granted, London is not on the whole the cheapest place in Europe.
I would tend to steer clear of Notting Hill - it's become incredibly gentrified around there, and that's reflected in the prices and explosion in overrated bars and restaurants there.
Brick Lane is great for Indian meals, as Tom G pointed out in his posting. the Begal Bake, at the north end of Brick Lane is good and extremely popular if you want a snack - it's open 24/7, and you can get a plain begal for 20pence, and a salmon and cream cheese for 90 pence (whereas you'd proabably pay £2 - £3 in the centre for the same thing). there are lots of good places to eat and drink that have recently sprung up in that part of town.
If you're in Soho, try Misato on Wardour Street for good cheap Japanese canteen style food, Pollo's on Wardour Street for ultra cheap Italian (£3 - £4 for a pizza or plate of pasta - the food's not amazing, but does the job if you're on a budget, and is pretty lively). Aurora off Brewer Street is also recommended.
High tea in grand hotels is always fun, but will burn a hole in your pocket. Fortnum's food hall is better than Harrods, and a bit less brash.
Pick up the Time Out Eating and Drinking guide, as that's a comprehensive and pretty reliable guide.
You can eat decently,delightfully and cheaply in London - you just have to look around a bit.