Which is easier or faster to get to by train from london?
Burton-on-Trent seems to be the nearest train station to Barton -under-Needwood. Burton-on-Trent is about 2 hrs by train from London (one or two train changes required), plus maybe 10 minutes by taxi for the 5 mile drive to Barton.
For schedules and fares, see http://www.nationalrail.co.uk/
I'm wondering why you would want to go to Barton Under Needwwood as there is next to nothing there. It's only a very small village off the A38. Perhaps though you have friends or family there.