Your library should stay intact for a short while, when switching subscriptions, unless you stay unsubscribed for a longer period. (Best to take a couple of screenshots, just in case…)
Bundled subscriptions are not administrated in your own iTunes subscriptions listing. Ask/instruct your carrier (EE) for a cancellation. How to cancel your Apple Music subscription with EE - EE Help
The subscription will end at the regular period (next due day; not immediately).
Re-signup for Apple Music, this time through Apple.
Get an Apple Music Student subscription - Apple Support
In Apple Music subscription options, select one of {Family, Individual, Individual (Year), Student}
After selecting Student, go through the verification process as instructed, so that the Music app gets to know what UNiDAYS knows. You may have to wait out the previous subscription to end.