Need to get from Southampton cruise terminal to Lancaster Gate hotel near Hyde Park. Ship docks at 7 a.m. Sunday morning.
Also, if you edit your title from the generic "Transportation" to something specific, like "Southampton port to Hyde Park hotel," you'll get better responses.
Get a taxi from the ship to Southampton Central railway station. There isn't a single "cruise port" as such, but all of the dock gates where you might come in are about a mile from the station. Southampton Central station to Waterloo, journey time around 1 hour 20 minutes. It's a South West Trains service, so check times and buy tickets on http://www.southwesttrains.co.uk/ . A cheaper alternative is the National Express bus. See the journey planner at www.nationalexpress.com. The Southampton coach station is about 500 metres from the railway station, the taxi driver will know exactly how to get there. Waterloo Station to Lancaster Gate by Underground - Jubilee Line to Bond Street, change to the Central Line to Lancaster Gate. If travelling by coach then you arrive at Victoria Coach Station, so that would be Victoria Line to Oxford Circus, then the Central Line to Lancaster Gate. Use the journey planner here: http://www.tfl.gov.uk/ You will need an Oyster card for Underground travel in London. Search this forum for hundreds of posts about them, where to buy them, what you do with them at the end of your trip, etc, etc, etc