I've never been at all confident in our Hmrc allocates payments despite payment reference numbers being used to confirm the period being paid. However, although I have clients running weekly payroll, they all pay monthly, based on the tax periods in payroll manager. Never had a problem with these clients. Because of the ability to use just monthly reference numbers, I am not sure Hmrc are geared up to weekly payments.
For another client, that I did not do the payroll for, just the bookkeeping, I have had to get them to request records from Hmrc on payments received and how they've been allocated in order to reconcile and then records were corrected. For another, it took a phone call to Hmrc.
I know this post is not a lot of help (sorry), but if and when you get it sorted, could your client move to paying for each tax period on monthly basis because I believe this may stop the differences.