If they check it at the door and say "not you uh uh"...
Come on guys! This won't be the only promo gig!
What do they check? How?
Best to ask amazon, it is their competition after all. There is an email address for questions listed in the rules. It is music-questions@amazon.co.uk
However the rules do clearly state that "To enter the prize-draw the entrant must submit their name, e-mail address, mailing address and phone number using the form above within the prize-draw period". So I guess the mailing address you provide will give them a big clue as to whether you are resident in the UK or not!
Also "No physical tickets will be issued. The name of each winner will be held on the door of the venue on the night of the gig. Entrant and guest must be 18 years or over. Photo ID (e.g. passport or driving license) may be required on entry".
But if you do not think they will be able to check, why not take a chance and enter and see what happens?