Your choices of airport into London are Heathrow and Gatwick, both are quite a long way from the city centre and I would strongly advise taking a train from the airport , and a taxi from the London Station.
I wouldn't advise anyone to hire a car FOR LONDON, traffic is terrible and the subway is a much cheaper and quicker option. You can get a one day "travelcard" ticket which is good for a whole days unlimited travel for about $5 per person ( this ticket is available after 09.30). Again for getting up to Nottingham I'd suggest a train to Nottingham city centre and , as long as it isn't too far, a taxi to collect your houseboat.
Travelling from London to DLP, I would strongly suggest taking the train, it goes direct to DLP and the station is positioned in between the park and the hotels. It's maybe 200 yards to the Magic Kingdom and 400 yards from trhe hotels. You can deposit your luggage at the station and they will take it to your hotel for you if you want to go straight into the parks, although if your booking on points you'll need to go and check into your hotel in order to collect your park passes.