In a hurry at the moment, so will just give a few.
First of all, you have to try the pubs. Many of them have some fairly decent fare, some do a nice joint (roast) on Sundays. Find one you like.
Rules restaurant, 35 Maiden Lane, Covent Garden, not far from the Strand. It claims to be the oldest London restaurant, it features game and traditional English food.
It is not inexpensive, but is not on the very pricey side. Men usually wear jackets. It can seem to us a bit stuffy, but the food is good and it is an experience. Have recommended it to many who have gone to London and have only heard raves. We often go there when in London (usually get there once or twice a year).
A sleeper, and one not very well known, is the Ognisko Polish Club, 55 Exhibition Rd, down the street from the Victoria and Albert Museum (a great place, no a must, to visit). It is in a Georgian house and well appointed. The food is Polish/continental and well done. Starters are from 7 to 10 pounds and most main courses are in the 11 to 16 pound range as I recall. Service is good. Wine menu is OK, not inspired. Google for menus and pictures.
OK, for cheap Polish, and we love the place even since the original owner died, and the place has been rebuilt since the fire, is Daquisse. It is a football field walk away from the South Kensington tube stop. Fancy, heck no. Decent grub, and quite inexpensive. Nice variety of vodkas.
O Fado, a Portuguese restaurant, 49 Beauchamp Place, a short walk from Harrod's is good. Got turned off a couple of years ago and have not been back since but the food was usually good and fairly inexpensive.
Have found the food court restaurants at Harrod's quite pricey. Tasty but not worth the pounds (which are going for about 2 bucks).
And our opinion of Simpson's on the Strand is not all that positive. As a carvery we find it somewhat overpriced and there are others about that serve traditional English food at least as good and for less money.
Just our opinion.
And then there are the pie shops (you have to try one), fish and chip shops (most of them are awful in my opinion, can usually find better F&C in pubs), and all sorts of ethnic foods.
Sure you will love the place.
But really gotta go. Have a great time.