This was my 7th cruise (Princess in '02, Celebrity in '04 & '06, NCL in '07, and RCCL twice in 2008). I traveled with my wife and three children (5, 4, and 2). With us were my parents (60s), my sister and her children (10 & 9), and my aunt.
We stayed in London at Le Meridien Piccadilly Circus for 2 nights pre-cruise. We used the underground to get from Heathrow to PC. That was really easy but there are stairs you have to negotiate (about 1 story worth of stairs). In London, we used the Ho-Ho buses but also did a lot of walking since PC is walking distance to Buckingham Palace, Trafalgar Square, Parliament/Big Ben, London Eye, etc. We watched the changing of the horse guards and found that to be really interesting because you can get really close to the guards on horses.
To get to Dover, we took taxies to Victoria Train Station, took the train to Dover, and then taxies to the port. Make sure you get into the right section of the train. After we got situated in the train, it was announced that the train would be split up before Dover and only the back half of the train would continue to Dover. It was a stressful chore to get all 11 of us and our luggage moved! So, ask about that if you take the train.