Having lived there for two years I know some nice places:
French:
the Ledbury is obviously a very safe choice, and top of the charts in almost any list of top restaurants in London. However, there is much more.
La Petite Maison (http://lpmlondon.co.uk/) - a very good bistro in London, Brooks Mews (not too far off Oxford Street). No michelin starred stuff, just good honest food. Highly recommended
Medlar (http://www.medlarrestaurant.co.uk/) - located in Chelsea, an ‘upper’ part of town, but I found this very fair money for the quality you get.
10 Greek Street (http://www.10greekstreet.com/) - depsite the name this is not Greek! It is very nice, but it is a small place and you will need to make a reservation. Prices are fair and dishes are excellent.
Le Gavroche (http://www.le-gavroche.co.uk/) - a very classic, two Michelin star restaurant in London. However, their lunch menu was perhaps the best value offering in London, so you might want to check it out.
The new Alain Ducasse at the Dorchester is quite good as well. But it is *** and located in a high-end hotel, so it ain’t cheap. That said, I have always found the tasting menu’s of the three Michelin starred restaurants in London priced substantially more attractive than eg the *** restaurants in Paris etc.
That said, many of the top end restaurants in London offer extremely attractive lunch menu’s so you could also check out Gordon Ramsey at Royal Hospital Road.
Japanese:
Zuma (www.zumarestaurant.com) - excellent Japanese restaurant, although perhaps the Sushi purists may find it a bit too fancy. You can book a table but we always prefered it to just show up just before lunch time and then be seated at the Sushi counter, for which they take no reservations. Be in time though, as otherwise the seats are all taken.
Italian:
Cecconi’s (http://www.cecconis.co.uk/) - a favorite of us when going for a late lunch or so. Italian food, and same applies here as for Zuma: you can book a table but we just always end up here around 1400 / 1430 and then wait for two seats to become available at the bar. We have some drinks at the bar and order some salad, a pasta, some other small bites. Always busy and always a good buzz. Excellent guy operating the coffee machine as well, you can see he takes pride in his job and they serve an excellent cappuccino / espresso / whatever you want
Zucca (http://www.zuccalondon.com/) - excellent Italian food, would go here for dinner though.
Tinello (http://www.tinello.co.uk/) - again, excellent Italian food, and (for London) quite fairly priced.
Zafferano (http://atozrestaurants.com/zafferano/) - a legend in London, so book in advance.
And another classic: http://www.rivercafe.co.uk/rc_page.php - it is a bit of a drive outside of the center of London, but well worth it.
And clearly Locanda Locatelli can’t miss from this list. Not cheap (it is a Michelin starred place) but very good. But you pay for the Damien Hirst artwork on the wall as well
If you are in or around Soho, stop at www.princi.com for a good Italian coffee, slice of pizza etc etc. Very nice and cool place. No bookings required.
Chinese
I always like Hakkasan, but every time I leave there I have the feeling I way overpaid… But it’s good food. For the best Dim Sum though go to a very traditional place called Royal Chine, I used to live in Bayswater too and this was very closeby for us. http://www2.royalchinagroup.biz/ and take the one in Queensway.
Breakfast:
For breakfast go to Ottolenghi, it is a simple place with very nice pastry etc etc. They have a couple of shops around London, so have a look at https://www.ottolenghi.co.uk/
And in Hyde Park you have the ‘Orangery’ where you can go for some scones, etc. Very nice and can be followed by a nice walk through the park.
I am sure I am missing a lot of things, but running out of time now. Will add later.