The Waldorf, at the end of The Strand (across the street from the Savoy).

Nice old-fashioned elegant place, not quite as overbearing as the Savoy and it's ilk but still 5-star. Key feature is the "Tea Dance" on Sunday afternoons; even if you are not staying at the hotel, book up and go to it if you are in to Edwardian elegance and dancing (and from the "old skool"!.

The hotel is also perfectly placed for walking to many of the key attractions if you wish.

http://www.heavenlyhotels.co.uk/meridien-waldorf.shtml

Having said all that, when we Londoners wish to have our own "romantic weekends" we tend to go out of London to country retreat places.