Forget about Hyde Park. It's an empty space where nothing happens (yes, yes Winter Wonderland was fine). The Regent's park is quite nice though, bring some nuts for the squirrels. But personally I'd avoid any parks in winter.

If walking is not a problem why don't you go on a guided tour around a part of London? I'd suggest taking any "Jack the Ripper" tour (well, not any - check the reviews beforehand!).

If he likes classical music and singing I'd take him to the Phantom Of The Opera or the Royal Opera House.

All the major museums are huge and there is no point in spending there just one day.

There are also quite nice 'afternoon tea' boat tours around London (aka City Cruises).