HMRC wrong pay dates and uc

Hi, I'm new here and just hoping for a little advice please . I've wrote in our UC journal but not had any replies and I'm worried .

Our assessment dates are 28th-27th

My husband was paid on the 28th Nov, 5th dec, 12th dec all correctly ,then the 19th he was paid two wks pay due to Xmas so the 19th pay was for the 19th and 26th but this was just recorded to HMRC as the 19th. Not really a problem as he then wasn't getting paid again until the 2nd jan. So the right amount of wages for the month was recorded . But then his work decided to pay him his 2nd Jan pay on the 30th deç which again was ok , until they recorded it as been paid on the 26 th Dec . So it now looks like he earned way to much in the assessment period. When infact he didn't . We've now received our UC for Jan and we're roughly about £450 down , I honestly don't know how we will manage . His pay roll is not open until Monday to discuss this . My understanding is that his payroll needs to contact HMRC and correct the dates . They will prob just tell him they can't do it, Can they refuse to do this ?? We have his payslip with the correct date and obviously the bank can confirm when his wages went in to . Once work have changed the dates with HMRC will UC amend our reward for the amount owing. ? If they don't and leave it as it is then next month it will also cause problems because then it will look like he's not earned enough and not meeting the aet. So although in full time work he will get calls etc. This isn't our fault and I'm worried sick it won't be sorted out. I'm reading that they will only move payments if you are paid monthly. Any advice I will greatly appreciate. Thankyou