Christ alive that's a lot of money!
Have you tried the AA website? I used a random 2017 astra reg number (came back as 1.6 diesel) and they quoted £212 to do the fronts and £196 for the rears. Which I still think is a lot, but a big chunk less than you were quoted. You have the option of a man in a nice yellow van doing it on your drive too - which sounds better to me than sitting in a freezing cold waiting room drinking sh!t coffee.
LINK TO AA WEBSITEJust for info, TPMS can be coded out for roughly £50 using a postal service (they send you a box to plug in, you do the update then send it back) so it will never appear again. Which would be my choice, like others I would argue that if you can't spot that your tyres are flat, you should hand back your licence.
LINK TO ONE SUCH SERVICETotal for the work doing the above way would be £450 ish - much more palatable