This ^^^^
And this ^^^^
WRT what Marky said, check the T&C's of your warranty to see what is, and what is not, included. Could the boot button be considered 'fair wear and tear'? Possibly, but my view is that you've bought a car from a main dealer, with an extended warranty, an item has failed in the warranty period, so needs to be returned to working order, and if that's by the warranty, then so be it.
I'm not sure I fully understand what the £120 is about? Is it a diagnostic fee? The boot button doesn't work - I'd have said that was diagnostics enough 🙄 Is the £120 for an hour's diagnostics? If so, how long will is take them to push a button and suss out it's not working.
I also think the clutch issue is something you take back to them, and ask them to remedy the issue, under warranty. Simple as that. Nothing more, nothing less.
It'll be the Consumer Rights Act (2015) rather than the Sale of Goods Act, but nevertheless I'm not sure asking you for £120 a pop is reasonable in either circumstance, so I'd suggest having a conversation with Trading Standards/Consumer Direct before going back to the garage, so you're better informed and know where you stand, because take you for a ride they will, if they can.
Gaz