Of course London has all the usual chain stores that you find anywhere in the UK, often with a better selection of goods than you find elsewhere, so if you have a favourite chain store it's worth checking out a London branch.
For shops specific to London, of course for real luxury and variety you can't beat Harrods. They sell everything, and while they are certainly expensive, quality is guaranteed. Selfridges is also great for Christmas shopping.
Otherwise it depends on the type of gifts you want. For food based gifts - which, if you aren't sure what to get, are always a good bet - Fortnum and Mason's can do everything from a posh hamper to a small luxury chocolate gift. For children's toys, Hamleys is still really special. If you're after something like a fine ornament, piece of furniture or glassware, try Liberty's.
For more individual and specialist shops and markets, you could have a look at the list here.