You will for sure need a hotel in London. I remember last year Sara (Edwina's Secretary) staying at a very nice hotel in London at Lancaster gate which was not too expensive.
And the London pass- check out under www.londonpass.com
If you decide not to go for the pass you would buy an Oyster card for transport- you load it up and it's much cheaper than single tube cards.

Go to a place where there is a big English cathedral- they are different from the French and very impressive. Places in the South would be: Salisbury, Winchester, Canterbury, Wells.
Go to see an English garden, e.g. Stourhead or , now I forgot how Virginia Woolf's garden was called.

England is fantastic .. but I think if you're there anyway why not consider Scotland as well?