The Stockpot cafe/restaurant in town does great pasta, roast dinners, and traditional meat and two veg type stuff, very super cheap and cheerful. Try not to get stuck in the basement though, it's well worth waiting for a window or corner table.
Wagamama - there are a number of them across central London is a good place to eat well on a budget. The bench seating isn't to everyone's taste but its good food served in a clean canteen environment by friendly staff
the place (dance school in euston) has a salad bar where you can pile your plate high for about £3 and get a tasty slice of quiche for about £2. Together they make a good meal. in a hurry there's ICCO pizza on goodge street. the hare and tortoise restaurants in the brunswick centre and elsewhere do main courses for about £5. some of them are huge.
Maoz on Old Compton Street for cheap healthy eats. Fill up your own salad box, add falafal, hummous ...
If you want to add a little unhealthy-ness to your healthy-ness add some belgian chips. Sit at the counter and people watch or take away and eat in soho square...
I like sandwiches for lunch and you can't beat the choice at Pret a Manger. They are located all over the city. On a nice day I take them away, eat in one of the parks, and share the bread crusts with the birds.
Tuk Tuk Thai Noodle Bar in Bayswater, opposite the tube station - quick service, pretty decent food and very cheap (main course & rice side & soda under £10). Tuk Tuk has other locations in London, too, though haven't tried them.
food hall on old street, next to shoreditch town hall, has a great menu that's updated almost every day, all dishes @ £6.
also japanese canteen near hoxton square has a bunch of tasty dishes around £5.
Near Piccadilly Circus you'll find Yoshino, one of the best and cheapest sushi places around. I always go to the venue at Shaftesbury Avenue which is take away only. You can fill yourself up of good sushi for under £4.
Beigel Bakery on Brick Lane, cheap and very fresh...I think they open almost 24/7 ;) freshly baked...I remember it's only around £0.30 per plain beigel...a few nice cafe around too...brick lane is another visiting point too....very artistic
If you are on a budget in London, the tourist attraction areas usually have places where you can have lunch for a tenner (£10). Also, look out for pubs where a meal is served. You will see their menu board outside onto the pavement. Pubs serve rather good food these days, you'll be surprised.
There's very good Thai on Chapel Market in Islington £3.50 small or £4.50 big. There's a few stalls but the best is from a small shop just off Chapel Market on the right hand side as you walk down from the Liverpool Road end of the market.