Lots of the middle eastern places open on Christmas Day, especially those near Marble Arch which is close to you. Might not be your thing, though.

Obviously all of the Park Lane hotel restaurants will be open. Might be worth trying Galvin at the Hilton (top floor, amazing views) or something at the Grosvenor House or Dorchester. (Four Seasons is closed for refurb.) You could also see if Theo Randall at the Intercontinental is open.

Time Out magazine often does a feature nearer Christmas on places open on Christmas Day .... you may want to keep an eye on their website.