For many types of debt (particularly in relation to Government departments), there is a 6 year cut-off period. (For example, the tax man won't normally seek payment after 6 years).
However, there are some exceptions. If the overpayment was due to an error by DWP, I doubt that they could claim any money back. But if the overpayment was due to an error on your part (such as forgetting to tell them about a change in your circumstances), they could argue that they were pursuing a debt incurred through fraud. In which case there is no time limit.
Chris