Top and bottom ball joints... re shim them.
Track rod ends, replace them.
Engine stabiliser bushes, engine mounts, replace them.
Rear Radius arms, swap them for reconditioned units.
Replace the bush ay the top of the steering column
I reckon on way less than £100 for that lot, and a morning to fit it all, car will handle like a go kart again!
EDIT Proper Mini, or new Mini Sam?

Thom