Have you, definitely, positively, absolutely, got the engine oil at the right level? If you let the oil get low, this is also just what the engine sounds like on start-up - presumably because there isn't enough oil getting to the tensioner to stop the slop.
If the bottom mark on the dip stick is 0 and the top mark is 100, then the oil level is at about 75%. I'm going to get some oil today and top it up to 100% and see how it sounds.
This is that 75% is with a cold engine which is how I have always checked oil in cars. The Mini manual which I have read this morning however, says you need to drive to operating temperature, then let it settle for 5 minutes before checking it, so I will do that after I've been to buy the correct oil.
isn't the car under warranty if you have just purchased it ?
It is, but I need to know whether I have a problem before taking it back. I am quite sure all I will get if I go back there without any info is, 'they all do that sir, it's normal'. I bought it from a Seat Dealer from their secondhand stock, so they probably won't know the common problems with the Mini.
Also the dealer is an hour away, so I don't want to go back just to let them listen to it then fob me off.
There are a lot of posts on this forum that claim ticking noises are normal on a Mini, some blaming fuel injectors, etc, etc.
They won't want to do any work under warranty if they don't have to, but I'm better armed if I can go back there and say something like "It's not normal, I have a problem with my with my Camchain tensioner".