Apparently the tradition started in Adelaide, Australia, with a "Magic Cave" set up in a department store in 1896, and the practice caught on in British stores. Nowadays, you can find a "Santa's Grotto" at most department stores and shopping centers in the UK. Kids queue up to see Santa and get a little gift. Grottos are not always free; some charge the equivalent of $5 or more (and presumably Father Christmas then gives the kids a nicer little gift.)
Families ready to grab their winter coats and off-season airfares can have a wonderful London Christmas that includes holiday lights at famous sights, outdoor skating rinks, Winterfest in Hyde Park, caroling, Christmas markets, and generally a good chance to imagine you're back in Christmas Past where Scrooge and Bob Cratchit walked the Victorian-era streets. London also has a gigantic New Year's Day parade.
As for Santa's Grottos in London... At top spots, Father Christmas runs a well-organized operation: Selfridges famous department store, for instance, has in-store Christmas entertainment, its own Santa Express train*, and online booking. Harrods and Hamley's have Santa's grottos too. Read more about Santa's Grottos, including reviews, at About.com's London Travel site.
- continue to Santa's Village, White Mountains, New Hampshire
*Always check for updates!