Yes, you can test it yourself. There are a few suppliers of home blood tests that provide this. The cheapest is Monitor My Health, which uses an NHS lab, so the results should be accepted by a GP:
https://monitormyhealth.org.uk/#
You can also check out Thriva and Medichecks, both of whom also offer HbA1c tests.
There is also a test called A1C now, which allows you to get the result pretty instantly, rather than sending to a lab. However, its a bit less accurate, and less you get it on offer, not a whole lot cheaper than monitor my health:
https://home.bhr.co.uk/a1cnowr-self-check-4-test-pack-cardiochek