The first step of disputing should be the 'Request to Reconsider Recovery of Overpayment' (RRR) form, also called a TC846. Download form TC846. A letter will do instead, but this form is quick and pretty easy. Do not spend too long filling it in, and in fact use question 11 on the form to demand answers rather than give too much details about your own defence.
Suggested content for RRR / TC846:
Take a copy and then get the form sent in by recorded delivery to the address at the top of the form as soon as you can.
If you are currently making repayments towards the overpayment stop them once you have returned this form. You can not be expected to repay while you are disputing the overpayment.
If HMRC hassle you for repayment or affect your current tax credit payments, complain, using our "Dispute Status" complaint letter; state that you are still in Dispute and as per their own Code of Practice (COP26) they should not be seeking to recover until this process has been exhausted.
This stage is only over if and when they write to inform you they have “decided not to write off the overpayment”. Until they make this statement, all the other external agencies you can present your case to will keep bouncing your case back to HMRC.
Now, immediately move on to Dispute Step 1b and Claim Your Data!