Don't leave it to the MOT man to decide tyres get a decent garage to check them if you don't know what your looking at (MOT man 1.6mm across centre 3/4 and no bulges splits exposing cords and looks correctly inflated .) Realistically in winter especially 3mm or less get them swapped....... I know my insurer look at MOT fails on your car and your premium reflects the condition of your car (it's public Access information)
Way I do it and it's a bit of leg work so to speak is pick the phone up and ring round local garages and do the
Eh up mate I'm ringing round what's the best price you can do on a 175/65r15 84T tyre (other sizes are available ) . And add any brand name or type that takes your fancy
Then check the shops website and often it's cheaper to book and pay on line
With my public service head on go for some proper all season tyres I've just had 2 new Bridgestone all weather tyres fitted (weather control Evo a005)
https://www.autoexpress.co.uk/product-g ... -test-2021 I'm impressed so far much stiffer than the nexens and the car doesn't twitch when you hit standing water
I've also Nexen all seasons and Maxxis ap3 all worked well on most conditions .... Unless you like the sporty drive afforded by sporty summer tyres.
Bit more info
https://www.youtube.com/watch?v=3N6PGrQ5imw