One of the weak points of the the MINI One and Cooper up to the facelift version in mid-2004 is the early failure of some of the Rover Midland 5-speed gearboxes, especially when tuned or driven hard.
Later MINI Ones and Coopers from about mid-2004 onwards were fitted with a stronger Getrag 5-speed gearbox but all Cooper S were always fitted with a 6-speed Getrag box.
The Midland box is no longer available new so even MINI dealers only fit reconditioned Rover boxes.
(The diesel Getrag gearbox is mated to a Toyota Yaris sourced engine so will not be a straight swap mating onto your petrol engine, so I suggest you source a later 5 speed One/Cooper Getrag or 6 speed Cooper S Getrag gearbox)
If you convert to the later Getrag box other parts must also be changed to match such as driveshafts, gearbox mounting, slave cylinder, clutch and flywheel,etc.
The 6-speed Cooper S Getrag can also be fitted in a similar way, used / secondhand boxes/driveshafts are often available from MINI breakers, etc, at least in the UK.
I have recently obtained a useful step by step 30 page PDF file (with photos & part No.s) on carrying out this conversion, so if you would like a copy PM me your email address and I will send you one.

(or anyone else thinking of doing this)