Clear immigration at Heathrow/Gatwick and transfer to central London by Heathrow Express/Heathrow Connect or taxi; gives you time to drop bags and freshen up.
Most museums and shops are closed on 25 Dec; the practical plan is a hotel Christmas breakfast/brunch or a prebooked Christmas lunch at your hotel or a restaurant operating a special menu.
Glasgow offers city celebrations and venues with music; if you prefer a quieter celebration, consider a hotel event or riverside spot. Book in advance.