I agree with Nick, at least 2 nights precruise in London , then travel to Southhampton by private charter, or 2 nights in London(at least) and then one night at the De Vere in Southhampton. I don't know yet whether I'll be staying at the hotel in London or with friends, so I'll be happy to go along with whatever the majority wants. I've stayed in several of the London hotels, so mostly you just want to get what is centrally located and nice. The London Eye is a great thing to do when its a clear day , as the views over London are great. I like the food halls at Harrods, the shopping is okay, I'm more of a Harvey Nicks store person, luckily, it's just down the street from Harrods. I think that for the history buffs, the British Museum(free entrance) is great for its Roman, Egyptian and Greek artifacts. http://www.britishmuseum.org/
Winston Churchill's underground cabinet war room bunkers are very interesting as well. http://cwr.iwm.org.uk/
The Tower of London http://www.hrp.org.uk/toweroflondon/
has a twilight tour that is great, especially is you combine it with the free Ceremony of the Keys which takes place at 9:53 p.m. every evening(it's a 10 minute thing) where they lock up all of the gates to the Tower as they have done for 700 years. You have to get tickets 2 months in advance for the ceremony, but it is free.
London Walks www.walks.com
is a respected tour company where guides take you on various walks around London where you get more on an insider's perspective on interesting things in London.
The London theatre is great, especially London comedies. They have great dialogue and great wit to them. London also has musicals that debut there first before coming to the U.S. It's a great way to spend an evening.
Everyone should go to a local pub, and have a pint!
I'll defer to the members who are locals about restaurant choices. There are numerous restaurants that are wonderful in London. TimeOut London http://www.timeout.com/london/
gives you a good overview of what's going on in London for the week.
The royal parks should be in full spring bloom, and are always great to walk through. I'll be just be happy visiting one of my favorite cities again.