@TGBB No, it won’t work. The reflective coating on the back of your cheap mirror is an all-or-nothing thing. If you scrape it off, you’re basically turning your mirror into a window.
Do some searching for a glass manufacturer. I know there are several people on this forum from the UK. Surely they can point you in the right direction. Worst case scenario, you can talk to your local glass shop / glazier and ask them to broker the purchase for you. That way you can depend upon their expertise in the industry to source the mirror for you.