Although all UC overpayments (including those caused by official error) are recoverable, that doesn't mean they should be recovered. Back in 2011, Chris Grayling (then Minister for Work and Pensions) told parliament, in connection with UC:
"The practical reality is that we do not have to recover money from people where official error has been made, and we do not intend, in many cases, to recover money where official error has been made. There will be an absolutely clear code of practice that will govern the circumstances in which recovery action will or will not be taken, to ensure consistent, considered decision making. "
https://publications.parliament.uk/pa/cm201011/cmpublic/welfare/110519/am/110519s01.htm
The government recently withdrew the relevant COP (code of practice from gov.uk) however. what of the undertaking given to parliament?
This leaves you with two options: 1) Complain, using the DWP's complaints procedure) referring to both of these points (the Minister's undertaking and the absence of guidance promised) and pointing out that the removal of the COP means you are unable effectively to argue your case and b) seek judicial review arguing that the DWP is fettering its discretion or failing to exercise discretion on recovery. A pre-action letter from a solicitor (if you qualify for legal aid) or welfare rights organisation can sometimes achieve a write off. If you are making a complaint, you may wish to do with with the assistance of your MP, given the fact that an undertaking was given to MPs about this.
I've seen a couple of letters recently where the DWP said that because the overpayment arose "as the result of official error" it would not be recovered.