You don't say which days you would be travelling on but if you are sailing on a Sunday then I strongly urge you to think twice about the train as track work is done on those days and diversions and/or bus service options between affected stations could occur. You can find details of proposed maintenance on www.nationalrail.co.uk. Cross country run hourly direct services from B'ham New Street to Southampton Central and normally take about 2hours 40 minutes. Look at www.trainline.co.uk I don't know the pickup point for Eavesway coaches (it could be Hilton Services on the M6 just north of you). I know people who have been very happy with the service but you should be aware that they are an independent company and, should the coach be delayed for any reason, the ship will not delay its sailing so, just as with the train, you should check your insurance cover re pre sailing delays. The advantage of the coach is that it drops you off right by the ship. Hope this helps.
We prefer going by train - How far is Southampton Central train station from the cruise terminals?
The Queen Elizabeth II Terminal is 2.2 miles away in the Eastern Docks, a taxi ride of about 10 minutes. Access to the Eastern Docks is via Dock gate 4. There are local taxis and Unilink buses that operate between Southampton Central rail station and the Eastern Docks.
The other 2 terminals are in the Western Docks, the City Cruise Terminal being 1 mile away and the Mayflower Terminal about 1.5 miles away, about 5 minutes taxi ride. Access to the Western Docks is via Dock Gate 10 and there are taxis available to take you the short 5 minute journey from the station costing approximately £6.00.