if they have changed the timing chain and have charged you for it and the fault is still there. they have not diagnosed the fault correctly and fixed it correctly so they are liable for all cost not 50% to rectify the problem. if they are admitting to 50% they no they have screwed up
speak to citizens advice they ail pretty much say the same.
carboning up of the valves is a know and big problem with the early r56 they revised the crank case ventilation on the later cars. and its normally the first place you look if you start to have problems
its nothing to do with bad fuel it just the way the positive crank case oil vent system works.
best thing is to install a catch tank and bypass all the system or mod
it as its been done here once its de coked http://www.mini2.com/forum/second-ge...se-delete.html
sorry i feel your pain all the best