Hotels - The Grosvenor House is an iconic London hotel, the Mayfair is not. As a local I cannot tell you about the quality of the rooms in either of them though.
Restaurants - Sunday Lunch -
It may be a bit obvious but had you thought of the Grand Divan at Simpsons in the Strand
http://www.simpsonsinthestrand.co.uk/restaurant.php which will be busy on a Sunday.
I like Hix on Brewer Street but have never been there for Sunday Lunch so cannot tell you what the atmosphere will be.
Le Caprice is always worth considering,
I have never had Sunday Lunch at the Grosvenor House but Michael Winner (a grumpy old food critic and erstwhile film director) used to rate it highly.