Sorry to say but yes.
If you don’t, the council will send bailiffs down to claim goods equal the amount owed. This nearly happened to me once.
I left my PGCE course years back and 2 years after leaving (and apparently them sending me notices, court summons etc…), they finally sent me an letter to my house (my actual home address). The reason why they didn’t do this before is “because they didn’t legally have to”, despite them having two addresses on their system and using only one… (my student accommodation address), despite me not being a student anymore… genius right?
In the end, the council where I attended said uni just ended up wiping it as it had been stupid long and too many blunders on their end as mentioned above!
You may be able to phone them and ask if you can pay it in instalments but that will be down to them (also, explain the situation about not finding employment yet).
Good luck!