Actually, it's overpaid and I'm due a refund - I could have switched to direct debit, but I didn't trust payroll to get it right (they have form on this...). As it happens it's lined up quite nicely with the conclusion of the saga and my new job.
Sorting it out was all rather straightforward - phone them up, give them the deductions from the past year's payslips (because HMRC only tell the student loans people once a year), and agree an account to pay the refund into which should turn up within the next week or two. I didn't even need to post them the payslips! The only slight wrinkle was they needed to confirm my bank account details from my university days but that was easy enough as I've got all the paperwork squirrelled away in a collection of ring binders.
Next on the todo list: sorting out tax codes and payments/refunds.