Joe,
The underdash handbrake is not known for its efficiency, so it needs to be in good order to get through an MoT. It's not difficult to strip down to free the button - BUT - take it apart carefully, noting how each part fits, 'cos it is a complete b*****d to reassemble.
Is the button actually stuck down, because it does screw in and out to adjust. If it is stuck down, and the cable itself is free - i.e. the handbrake works, but just won't lock, then either its been pushed in too far, and you'll have to dismount it and push the button out, or the spring that pushes the button out has become misplaced.
I doubt Caterham will stock them now - give Mick at Redline a call on 01883 346515, they stock almost everything for the older Seven, and should be able to help.
Dave H