Going on a cruise out of Southhampton. Will be first staying a couple of nights in London near Paddington Station at London Lancaster hotel. Any suggestions on bus or train service from Hotel to port in Southhampton? Then on return, I will end transport from Southhampton port to Heathrow. There will be 4 of us.

You should find lots of info here: http://www.londontoolkit.com/travel/...e_terminal.htm

Have you considered taking a taxi? It would be a little bit expensive, but it is the easiest way.

A taxi from London to Southampton? You have to be kidding. Or a taxi driver....

Check out Megatrain / Megabus. Very inexpensive transportation from Waterloo train station to Southampton. You pre-purchase thru their website. Then from Southampton we booked a minivan with 2 other couples from our ship (made connection thru the roll call on Cruise Critic) and it ended up being very reasonable - about 30 GBP per couple!

A taxi might cost almost as much as the cruise!

Thanks, I'll look into these.