Nobody has mentioned Rousillon in Chelsea which is great. Would also second the Landau near Oxford Circus. Of course, there is Gordan Ramsey at Chelsea. Many top quality fine dining restaurants in London really; depending on which area you prefer.

Should not be too difficult to get a table in January due to
1) recovery from the excesses of Christmas and New Year
2) credit crunch means less business entertainment and end-end personal treats.

Just book ahead.

For the single diner; I would say
1) the Landau
2) St Alban's near Picadilly Circus
3) a seat at the bar at L'Atelier de Joel Robuchon just beside China Town (half the seats in the restaurants are at the bar!)