Also - forgot about this - A day out in Brighton is also a thought, trains run every 15mins from Victoria (45min-1hr journey). Brighton is very compact & walkable (& very shoppable). Head for the seafront & smell the sea & get blown along the front (can't do this in Switz!).

Visit the Palace pier for the fun rides, candy floss, donuts etc. The Royal Pavilion is fab with its own guidebook for children, you can see what the nutty British royalty spent its cash on.

Visit the Lanes & North Laine for lots of quirky/funky shops with interesting places to eat there too. Churchill Square for more retail therapy.

Afternoon tea in the Grand or the Metropole Hotel.

Fish & chips out of the newspaper.

Personally I wouldn't bother with shopping in London (esp with a 6yr old) at that time of the year - its a cattle market, just go & do the sights & have loads of fun.

A wetsuit & canoe may also be useful items in your luggage.