Savings

I know I have previously posted but recently my husband got the unexpected ESA letter saying he might be owed premium payments, after looking into it I have found out you are only allowed £6,000 allowed for savings , but since march this year his and mine savings have gone over this amount and I have found out it is £1.00 for every £250 over the £6,000 is this from week to week ? it usually exceeds this especially when his pip money goes in , he saves his money to renew his car every 4 to 5 year as he is dependent on it , should I inform them about it as my husband and I had no idea this was the case he says he will willingly pay any money owed but was wanting some genuine advice on what to do . Since telling him he is worried sick about it and is getting really agitated about the whole matter, his ESA was the contribution based one and he was put in a support group due to his physical and psychological condition .
Thank you once again
Carol.