All travellers to London should take advantage of the city’s excellent international fare.  The ethnic cuisines available in the city are AMAZING thanks to the diversity of the city's residents. Try to incorporate one of each of theses cuisines to experience the full spectrum of what London has to offer: pub food, Thai, Indian, Mediterranean, Chinese/Japanese, Italian, French, and anything else that suits your taste!  In such an international city, it would be silly not to take advantage of the variety of cuisines.

Once you have chosen your hotel, do an internet search for a "London restaurant guide."  Most of those sites allow you to screen restaurants by neighborhood, so you can find great places to eat near where you are staying, or if you know you will be touring a certain area, restaurants there.  www.london-eating.co.uk is a reallly good site, where you can also read candid reviews by people who have tried the restaurants. For certain restaurants you can also book a table through this site and take advantage of special offers.

Another good source for comprehensive restaurant listings is www.timeout.com/london/restaurants/. You can search London restaurants by type of cuisine, location, and special features such as "budget" and "critics' choice." Each listing has a compele description including prices and special features, opening hours and a link to a detailed map showing exact location in London's complicated street system.

Try some of London’s top restaurants at reduced prices via Toptable.  They have some amazing deals and if you register with them before your trip they will email you with current offers.  You can search by cuisine or various other categories. Take a look; it’s well worth it.

Pub dining can vary greatly in price and quality but generally you can never go too far wrong as long as there is reasonable ale to wash it down!  A great pub in the Kensington neighborhood is the Hereford Arms. They have a great menu; you should try the fish and chips or their special of the day. The ambience is very British and the help is very friendly. And they even have a small "no smoking" section!

Belgo in Covent Garden is also awesome. Great beer, better mussels and fries.  Give it a shot.  The modern atmosphere and waiters dressed as monks make it an interesting night out.

One of the best inexpensive dining experiences in central London is the Indian Restaurant Chowki just off Picadilly Circus.

If you want to have some money left over to splurge on dinner, try grabbing an affordable breakfast and/or lunch at Marks & Spencer, Sainsbury or Tesco.  These ubiquitous grocery stores have a wide variety of sandwiches, drinks and snacks to carry you through the day. Dining in London can be an expensive proposition, but you can definitely save a bit with this tip.  Plus, it’s fun to browse in a local grocery store and see what interesting products you can find that are different from home! 

Also, some suggestions from this forum thread include:

Cafe Espana in Old Compton Rd, Soho, is fantastic for tapas.

Made in Italy on the Kings road in Chelsea is excellent for Pizza. Around £8 each.

For dim sum / yum cha, New World restaurant in Chinatown - off the main strip in Gerrard place.

Stockpot in Panton Street, just off Leicester Square. Its basic, but good, with main courses and salads for between £3-£5. There are a few reasonable pizza deals around Leicester Sqaure too, such as a lunchtime buffet for around £5.

Porters on Henrietta Street in Covent Garden is a decent spot.

For Italian, "Ask" gets good reviews. They have several locations. Also, with several locations is "Spaghetti House."

Cafe in the Crypt, and Wagamama are inexpensive favourites!