from my own experience of being made redundant and the effect on benefits many years ago, the explaination went along the lines of
"the redundancy payment is a compensation payment in lieu of salary, Therefore you are being paid for work that you would have done"
This is normally higher than you would get for the equivalent time on benefit.
Many people think of redundancy payments as a nest egg from the Golden Goose and try to save and protect it. It's not, it is a buffer for you to live on!
Unfortunately you cannot get paid twice for the same time periods, so it is possibly better to live off the redundancy payment for the period and during that time, prepare claims for when your redundancy money expires.
Be prepared to show financial evidence, bank accts etc that you have spent your redundancy.
BEWARE, do not splash out and spend all your redundancy on expensive goods or holidays as the benefits office will call this "deliberate degradation of capital" and will delay amy benefit payments