Hi Seb have a look at
www.theminiforum.co.uk , they have a subforum on spi problems which will give you an idea where to look. The symptoms you describe suggest a vacuum leak .
At the back of the inlet manifold there 2 vacuum lines,1 to the air filter & the other to a small black box (the fuel trap,one line in & one out to the ecu). These vacuum lines connect with small plastic elbows which are notorious for small cracks that are hard to see.
There is also a metal pipe manifold that connects the engine breathers & the charcoal canister to the front of the throttle body using rubber hoses which can also crack & perish.
Another cause for poor running I have encountered is a build-up of debris on the crank sensor located under the starter motor. This is easy to remove & clean.
I hope this helps, Cheers Phil.