1. The payment went to the wrong month
UK PAYE runs on tax months, and a tax month runs from the 6th of one month to the 5th of the next. Month 1 is 6 April to 5 May. That is already out of step with your calendar and your bank feed, which is where a lot of this starts.
Your Accounts Office reference is thirteen characters and it identifies the employer, not the period. On an ordinary payment arriving in its normal window, HMRC works out the period from when the money turns up. Pay early, pay late, or clear two months in one transfer, and it has to be told, which is what the four extra digits on the end are for.
The tell. Your total paid across the year looks right, but one month shows arrears and another shows a credit of a suspiciously similar size.
2. The submission carries the wrong pay date
This is the first item on HMRC's own list of reasons a PAYE bill is not what you expected, and it is the easiest one to make. A charge falls in the tax month of the pay date you reported, not the date you sent the report. A payday of 4 April belongs to the tax month ending 5 April even if you filed it a fortnight later, and a payday of 6 April belongs to the next one. Put the wrong date on the Full Payment Submission and the whole charge moves months with it.
The tell. Two consecutive months are wrong by roughly the same amount in opposite directions, and the pay date on the submission does not match the date on the payslip.
3. A reduction was never reported, or went in late
Some things reduce what you owe, and none of them apply themselves. Statutory maternity or paternity pay you are entitled to recover, Construction Industry Scheme deductions suffered, the Employment Allowance: HMRC learns about all of it from an Employer Payment Summary and from nowhere else. Send no EPS and the charge stands at the full figure from your Full Payment Submission, which is exactly the number that gets demanded.
Timing counts as much as content here. A reduction only comes off the current month if the EPS reaches HMRC before the 19th of that tax month. File it on the 20th and the relief is real and the money is right, but the month still reads as unpaid until the next bill catches up.
The tell. The shortfall is close to a figure you recognise, because it is the relief you thought you had already claimed.
4. One employee is on the system twice
Every employee needs a payroll ID and it needs to stay theirs. Change payroll software, renumber the staff list, or reuse an ID that once belonged to a leaver, and HMRC can open a second employment record for the same person. The pay gets counted twice, and so does the tax on it.
If you are giving somebody a new payroll ID, set the payroll ID change indicator so the old record and the new one are joined up. Without it your software is reporting a new starter as far as HMRC is concerned. Duplicates are often cleared once later submissions land, which is why the order below says check, then wait a little, rather than phone immediately.
The tell. The demand is not slightly wrong, it is wildly wrong, and the excess is about one person's worth of tax.