When I'm in London for the day I tend to one of two favourites - both likely off the tourist radar.
More times than not we wind up at the Soho location of Wahaca, an Anglo-Mexican-Mexican chain which specializes in sort of Mexican (specifically Oaxaca - see how they changed the spelling) street food and tequila. We particularly like the Wardour Street (Soho) location because of the fun toilets downstairs, the window views onto a typical Georgian lane, the staff is always on, and the nosh is pretty tasty - especially for my Texan expat wife.
If we don't pop into Wahaca we usually find ourselves just around the corner at the New World for Dim Sum. It is on the corner of Shaftsbury Avenue and Gerrard Lane on the border between Chinatown and Soho. The dim sum is not the very best in the world, and maybe not even in London, but it comes on little trolleys so you can just point and try. Beside the New World there is only one other London dim sum place still using trolleys. The staff, some we have seen there for over 10 years, know what they are doing and the food is fresh and tasty. Service is fast.
Certainly if you have a couple of pound notes to rub together you should be able to find something tasty in Soho. Just on Wardour Street there's also Busaba Eathai for excellent long-table Thai, Princi for fabulous long-table Italian, the Swiss resaturant, several Jerk joints towards Oxford Street, and many more I haven't listed. Branch out a street or two on Deane Street, Frith Street and the rest of Soho there are hundreds of top-notch places I don't have room for. Don't forget Bar Italia. Gelupo's not far off either, quite close to the first suggestion by Claudia above.