This is why we need specifics. The OP might be staying near Trafalgar Square, or perhaps in Pimlico - they are different areas. We have no clue what sort of food the OP likes, or what is considered romantic.

Simpsons and the Savoy are expense account and not really romantic. Poule au Pot is hot and sweaty but could be considered romantic by some. None are about the food but they do all have memorable atmospheres.

I still think that the purchase of a Zagat would be the best investment. Online is not much use in this sphere except to use Citymapper for transport options.