Cancer is not listed as a valid reason to get a flu jab on the NHS, so just like with anyone not on the list of illnesses or circumstances, an NHS one is at the discretion of the GP.
I get a free one on two other basis on the list, including being a carer, but not due to having prostate cancer.
By the way, never had to get the form signed by my GP - I just do it in the chemist, but that only works if you fit the circumstances on the list.
If you're not entitled to one on the NHS, you can still buy one for around £12.
I do take a note of the flu jab lot no., batch no., and expiry date, and pass that on to my GP, and they stick it on my record. (Without the lot no., batch no., and expiry date, their system won't let them enter it onto my medical record.) In theory, Boots should tell the GP, but that's never worked.