Thanks everyone for the ensuing discussions - it feels good that I'm not alone and can get some balanced views on my predicament.
I paid a deposit and then signed up to a 4yr lease agreement. If I chose to terminate on a whim (as opposed to asserting that the car was not fit for purpose) it would immediately cost me 50% of the value of the car, i.e. £8k. Which I couldn't afford to do.
However - the car, to my mind and I'm sure to others, too, is NOT fit for purpose given that it has the issues that it does.
Yes, my dealership has been pretty shoddy so far and their immediate reaction (for those of you who don't want to scroll back through the threads to find my original post) was to be highly defensive, maintain that other customers in much hillier climbs have not complained, and I could discuss changing the vehicle to a different model, i.e. the 1.3, TwinAir or diesel.
There was no acknowledgement of my disappointment, no offer of an apology, and no suggestion that I should bring it back to them for a full diagnostics straight away. In fact, this latter fact astounded Fiat UK when I phoned them the first time, as dealerships should ALWAYS offer this in these situations. It shouldn't take me to harangue them with lots of unreturned phone calls to get the tests scheduled.
My query now is what I do from here. I think, given that I have done everything by the book as far as Fiat UK is concerned, I need to phone them every week now and document when and what was said. Whilst I'm not in the slightest bit impressed with the dealership, I have to agree that they are somewhat in the middle. Yes they took a deposit, but my financing is between myself and the finance company, who incidentally I have NOT contacted yet, but would be keen to hear from anyone engaged in a similar lease agreement who HAS.