Happy Christmas to you!!
No, the tube only goes as far as Wimbledon in that direction so you'll need to get the mainline service. It's a direct service from Waterloo which makes quite a few stops, but you won't have to change so it is easy. If I remember rightly there's a train every half hour. Hampton Court is the end of the (short) line so you can't go too far.
(You could get the tube to Wimbledon and pick up the Hampton Court train there as the tube and mainline share a station at that point, but I think it would be easier to go from Waterloo.)
Libby