also are you running synthetic motor oil?  It doesn't smoke when it burns so maybe you have some water in your exhaust with an oil consumption problem too.   Look at your engine oil. Conventional motor oil with water in it looks milky.  Not sure if it's evident on the synthetic oil.

yeah, test the compression and leak down. Also a puff of smoke leaving a stop is guide seals.  Leaking from the top. Is it constant smoke?  how many miles on your engine?  Also Marvel Mystery Oil cuts carbon on rings and restores compression. Read the can. Add to oil and gas.

Good advice from spank.

Have you tried a leak-down test?

The R53 Cooper S and JCW uses the same pistons and rings....

Rings can wear out he ring land (groove) of the piston. I'm not sure how robust the BINI (BMW MINI) pistons are, but stock-ish aftermarket replacement pistons probably can't be much more than the price of some factory rings.

You really won't know what you need until you pull it apart and have a machine shop hone your block, measuring it for size to see if you have worn a taper or oval in the bores. If you've been smoking for a good bit while driving, there's a chance you have scored cylinder walls that might not clean up with just a hone.

Hi everyone, hoping to get a bit of advice , my R53 is using about a litre of oil every 800miles and takes a few turns to start apart from that and the blue smoke it’s ok, I’m assuming the rings have gone but I’m trying to decide whether to get a set of rings or a set of JCW pistons with rings which only cost £200