Is the garage a Mini specialist and use BMW/Mini specific code readers ?
If they did a compression test, one would presume they have removed the error codes this creates.
What was the sensor error code given by the test equipment ? a Lambda Fast Idle test score of 1.24 isn't very helpful as it could be a major issue or a minor issue causing problems (hence the need for the ECU Error code).
I don't know what you pay for cars in the UK but if its been a solid car up to date, you have the time and money and capability, why not get it fixed, its a 2001 Cooper and there wont be that many around and more going to the scrap yard every year. I wish to heck I had held onto my Morris 850 many many years ago as it would be worth a mint today in a full restored condition.
My R50 was built in 2001 but considered a 2002 Cooper, It lets me know its around and gives me grief from time to time but until circumstances dictate, I wont be getting rid of it any time soon or in the foreseeable future. I can honestly say, I can never decide between my R50 and R53, both have thier quirks but the R50 is still putting a smile on my face.