Most garages would fit an exchange reconditioned gearbox rather than rebuild it themselves. If you search on MINI2 there are a few replacement options available.
Here is link to recon box from MiniMatt :-
** RECONDITIONED ** BMW MINI GEARBOX 00/04 on eBay, also, Mini, Car Parts, Cars, Parts Vehicles (end time 01-May-08 11:19:07 BST)
The early Ones and Cooper Midland gearbox are prone to failure so fitting a secondhand used gearbox would have no long term guarantee.