If you are still getting tax credits the recovery is dealt with by deduction from them. If you are not, then they ask for the money back straight away or over 12 months. However, if you can provide an income & expenditure statement showing you cannot afford to pay over 12 months and make an offer to pay over a longer period, then they should accept it (providing your figures are reasonable and you are not living an expensive lifestyle - & it appears from your post that you are not).
They can be difficult to deal with - if there is a CAB near you it could be worth consulting them for help. They can also advise you on whether you do actually owe all the overpayment you are being asked for.
This can be a complex subject and the Tax Credit Office is certainly not infallible, so don't adopt the attitude that you can't fight them. You certainly should not accept the amount of the overpayment without being given a proper breakdown of how the figure has been calculated, so ask for this.
If you haven't already got it, ask for their code of practice COP26 which gives information about overpayments and the circumstances in which they are considered to be recoverable. Then see how the reason for your overpayment relates to the information in the booklet.