do they have on site tours or guides at Hampton Court or should you book one through a tour company in London?
You can take train to Hampton Court. They have at least 2 tours you can book right there. Tudor Era, Jacobian Era and maybe Georgian? It probably depends on whether it is a busy time or not if you need to book ahead. You can take a boat back to London if you time it right. Look them up on line. You can even stay there.
There is a numbered trail taking you through all the exhibits. At this minute i cant remember whether you can get an audio tape guide or whether it is all on a written guide you take with you. Someone here is sure to remember. You dont really need a human guide to get around, although it would probably add to the experience. Most people do without a human guide
An audio guide is included in the ticket price. There are docents located throughout the Palace who will give you extra information. Here is their website, it will help you plan your visit and includes suggested itineraries. http://www.hrp.org.uk/HamptonCourtPalace/
If you're coming from Central London, do look at taking the opportunity of travelling on the river for part of the trip there or back. You can pick up a boat at Richmond. (Taking the boat from Central London can take 3/4 hours).