Same situation as you but cruising next August. Also our first trip to Europe. Based on some great info from John Bull and others here, we will probably use National Express from Heathrow to Southampton and taxi to Premier Inn West Quay for two or three nights prior to cruise. Wife would like a day of London so we will probably take the train from Southampton back to London Waterloo Station and do the Big Bus HOHO. She has mobility issues and the less bags I have to schlep for us both works for me.
If we were to stay in London two nights before heading to port, I would stay at Premier Inn Waterloo then train to Southampton. Sorry to hijack your post. Hope you get the info you need.