Romantic dinner with a view over the Thames river.

A few options for you. Firstly, Pont de la Tour is good. Personally I prefer  Butlers Wharf Chop House which is next door to Pont. Book early and ask for a view of the bridge.

Oxo Tower Bar is also very nice, with views of St Pauls.

A bit of a curve ball, you can also do a river cruise from near westminster. It takes around 2 hours and you get a 3 course dinner. There are a few different companies that do it.

Finally, you could look at the Heron Tower near liverpool street. There are a couple of restaurants there including sushi samba. http://www.tripadvisor.co.uk/Restaurant_Review-g186338-d3381993-Reviews-Sushisamba-London_England.html

The Cutty Sark Tavern pub in Greenwich (4 Ballast Quay, SE10 9PD) is a 17th Century building, with a lovely view over the  The O2 Arena or "The Dome" and the Canary Wharf. It has a nice restaurant with an good menu. Book a table up in the top room, which is called "The Crow's Nest" and has the best view!

Le Pont de La Tour: Restaurant is a wonderful, romantic reston the south bank, just down from Tower Bridge www.lepontdelatour.co.uk

The Oxo Tower Bar is beautiful and perfect for a fancy occasion. It's pricey but worth it and completely memorable. 

Don't forget cafe options overlooking the Thames at the Tate Modern! A nice place to grab a drink and take in some art. 

Enjoy!

Great answers provided here for central London. For an alternative worth considering, look just a little further up river at Maidenhead with the Boulters Restaurant on Boulter's Lock