We have travelled with Cunard many times and find the best way Manchester/Southampton is by Virgin Trains just telephone regularly andyou will be surprised how the fares get lower and lower.
As you are with cunard the brochure recommend cruise connect as they go to most places, or if you prefer train travel if you wish to have more comfort they woul probably go there but you would need to change trains, so bus might be easier.
The best way is to get a friend to meet you and take you there. The next best way is to get a taxi but this is expensive. Rent a car is an option, one where you can leave the car in Manchester after a pick up in Southampton. Next is the train which if booked at the right time can be reasonable in price and last and the most economic and maybe the best overall is by National Express or by one of the arranged buses. This might be a bit confusing but you can find out times and prices on the www. and then you can see where your priorities lie. .... Neil.
As well as Neils suggestions...flybe fly to Manchester from Southampton airport which is not too far by taxi from the port (I'm assuming you will have left your car at Manchester airport???).
The best and most convenient way is to have a chauffeur meet you and take you to your destination. Cheaper yet still convenient options are to take the train or fly.
Virgin trains are currently offering a direct service Southampton to Manchester every 15 mins past the hour. Takes about 4.5 hours and an advance single standard class from 10.15 onwards is £32.50 each. You can't book more than 12 weeks in advance so things can change from now until then. www.virgintrains.co.uk (Don't use trainline, they charge a booking fee for no good reason). Hope this helps.
I have been unable to find a direct train manchester to southampton for some time. #Dont know how you would do the clevelys bit but we regularly do the trip from Wigan. Easiest is to change at Birmingham and request assistance in advance by phone. This is available for all, and you are met at the train and taken to a waiting area and given help with luggage. We have even been taken to the taxi at Southampton. Fares at times have been very cheap. Search trainline.co.uk for information, and if you dont wish to pay booking charge get the tickets at your local station. Good luck.
There are definitely direct trains to Manchester every hour i.e no change required enroute. The other option is to use the Cunard coach connect service. A one way car rental can also be cost effective and there are car rental companies in the port.
The best way to get from southampton to manchester is to use the Virgin Cross country which is frequent and quite reasonable taxis from the pier to the stationis about five minutes.
I would certainly recommend the Cruise Connect option. We travelled down to Southamtpon from Warrington on a Saturday morning. We left at 7am and arrived at approx 1:15pm. Our check in time was at 3pm, but we were on the QM2 by 2:15pm. It is a care free easy option with regular stops to ease the journey and we are doing it this way again this year, both from and to Warrington. We hope you have a wonderful time. We thoroughly enjoyed our transatlantic voyage.