Steve,
If I remember right and if your 2010 is the same as my 2007 4 seater, then you can fold the back seat down to reveal a couple of press stud fixings that hold the seat leather in place; with these removed I think you should be able to see a couple of screws which when removed will allow you to slide the seat bottom forward. There is no need to go under the car or to remove any of the carpet.
As a new Morgan fanatic, fitting a new battery was one of the first tasks I had to do when the original '07 battery died a instant chemical death when I was driving down a country road with my daughter. Thank goodness Morgan's don't rely on electric power for much

Cheers
Richard