3 great recommendations:

J Sheekey in Leicester square - one of the best in london, pricey but if you order well you can keep it together

La Pont De La Tour - a really interesting place in butler's wharf, across the thames from central london - you can get out of there fairly reasonably and the view of the tower bridge is unbelievable - if weather is nice a table outside looking up at the bridge watching the boats float by is one of my favorite things to do in london

If you really are on a budget and can not pay 20+ pounds for an entree try Livebait, the have several around but teh one in covent garden is quite good

Have fun!