Haven't RTFT, but:
Ring them straight away and explain that you haven't received carer's allowance since 2016. Refer them to the bank statements that you submitted in support of your UC application, these will show that you are not receiving carer's allowance. Ask them to reassess your claim as a matter of urgency, because they have made a mistake.
Check the dates for both the period covered by the last HB payment (on your payment advice) and the start date of the UC claim (on the UC award letter). If they don't overlap, you may be able to get the full payment reinstated.
Final HB payments are often made after the UC claim has started, because of the time it takes to close down claims. DWP don't quite get this, and count it as income for the UC period. I have had some success in explaining to them that it is an arrears payment, and should not therefore count as income during the period for which UC was claimed.
Are they they claiming back all the overpayment because of the overlap between housing benefit and universal credit in one hit? If so, explain that this is causing you hardship and ask if it can be repaid by instalments at the maximum rate, which is around £11-12 pw.
Also, if any overpayment has been caused by a mistake on the part of the DWP, you can challenge the decision on the grounds that it was their fault and that it would be unreasonable for them to recover the money and cause you hardship.
UC has been rushed through and staff have not received sufficient training, so mistakes happen a lot. There is also a real lack of consistency when decisions are made, which makes it hard to give advice sometimes. There are a lot of scenarios that aren't covered in the decision maker's guidance manual, simply because no-one ever thought of the implications of stuff like switching from SSP + HB to UC, and how to treat post-closure HB payments.
They should have asked a few benefit advisers to look at pitfalls, but of course this govt doesn't give a toss about people on benefits.