Had very similar issues with my 1.2TSI, and equally poor service from the main dealer.
After getting sick of the endless "oh this is the first time we've ever seen an issue like this" charade and waiting around for parts, I went through SEAT UK customer service who eventually resolved the issue (albeit I was still out of pocket even after goodwill). Shortly after the gearbox lunched itself and I got rid.
Never again. I know everybody says this after a bad car experience, but the attitude of the dealership bordered on comical. Definitely feeling your pain.
Same happened with my Ibiza. Owned it a week and the waterpump cracked. Took them just over a week to fix it because "parts only get delivered on a Tuesday" and they tried to charge me £500 for it, even though I just bought extra warranty for it. Funnily enough when I complained to SEAT UK their deliveries were all of the sudden upgraded to daily and I had a bill for £0.