I used to work for DWP. First of all they will adjust your claim so they pay you the right amount going forward, based on your current circumstances. It may be some time before they calculate your overpayment. Before they do this there is every chance you will be asked to attend a job centre for a compliance interview. It isn't an interview under caution and you won't have a criminal record. It's to check if there is any reason why you didn't notify them (which as you've already said is because you didn't realise would be "mistake".)
As the welfare reform act puts the claimant liable to repay any overpayment regardless of whether it was caused by them or DWP (official error) you will have to repay it. Previously, the social security administration act classified overpayment into 3 categories - official error, mistake, fraud. Official errors didn't need to be repaid. The meeting- which may take place by phone post-covid - is to gather information on how to classify the overpayment or to bring any evidence as to why it isn't an overpayment (which in your case doesn't apply). If you did it on purpose it would be fraud and that would be treated differently. As they have no evidence yours will be classed as mistake (failure to notify) and unless you have a medical condition or recent bereavement that meant you were out of sorts and couldn't possibly tell them at the time, you will get a £50 civil penalty added to the amount to be repaid. They say this is a deterrent. You won't find out if you'll get one of these until they send you the letter notifying of the overpayment. It could be months before you hear about paying it back.
You will start to get automatic deductions shown in your journal for about £50 a month per debt (per period of overpayment). The civil penalty loads onto the system as a separate debt and is repaid first. You can end up repaying several debts at once. If you can't afford the deducted amount, call DWP debt management as soon as you are notified and ask to reduce the deductions. They may ask for income and expenditure. As your overpayment won't be classed as fraud the rules for reducing aren't as strict as they would otherwise be (for fraud , one of the reasons you can have it reduced is if your doctor provides a note to say you are starving. I'm not exaggerating.) For mistake overpayments it's if you can't meet your regular outgoings. Similarly, if you feel you can pay more or pay in a lump sum to get it out of the way you can do. They can't reduce the amount of the first deduction. Once that's been calculated, that's the amount you will get deducted that month. They have no facility to change it. I used to set the deductions and it felt a bit evil, especially as people aren't notified in advance.
You won't have a criminal record or anything. It doesn't affect your credit rating or ability to claim in future. The debt won't go away though. Benefits aren't paid under the consumer credit act therefore the debt doesn't become statute barred. If you stop claiming and don't pay they write to your employer to take up to 40% of earnings, take out of other benefits, or even your pension if you never earn or claim again until then.
Sorry got carried away there. It's pretty much the only thing I know anything about.
TLDR don't worry.