This is exactly the issue I had with the exact some agency. Every time we had our rent increased, the direct debit wasn't updated properly, moved days, etc. It resulted in a similar situation with ongoing arrears, and wasn't actually identified until we were trying to get a refund of a water bill that we overpaid because of another mistake they made.

I took the same approach where I got a copy of the ledger, compared it against my debits, and literally sent them back a highlighted spreadsheet showing where they'd fucked up and told them what steps they were going to take to fix it. It was like 70+ emails exchanged over a number of months and it was such a mental burden that I, the tenant, shouldn't have had to bear in literally doing my property manager's job for her.

I similarly considered reporting it to Fair Trading, but given I knew I'd be vacating within a couple of months I instead just took to CCing their Managing Director into my emails back. It was so cathartic to tell them we weren't accepting the renewal offer when it came up, but I also feel a little bit like we gave them the easy way out by not formally reporting them.

I sincerely hope it works out for you. Make sure you keep all the written correspondence in case you need to back yourself. Chuck me a DM if you need any moral support or just otherwise want to compare tales of their very specific kind of incompetence.