I think it must be a screw up by your company's payroll. I'm trying to think of scenarios that could cause this.

1) A 'Payment after leaving' flag was set in the payroll software. This causes tax to be calculated using the code 0T (no tax). In this case, depending if they set it as a regular payment or not, your NI may be calculated using weekly calculations or monthly calculations (There is a distinction, the thresholds for weekly calculated are not just the monthly thresholds / 4).

2) They had the wrong tax to date figure keyed in from your P45 or recieved via the P6/P9 process. That seems unlikely though, as it would have to be an exactly too large figure to cause zero tax, it would usually just cause a wrong amount. Perhaps if they didn't allow refunds (made them zero tax instead) this could happen, but I've never heard of that being a policy anywhere.

3) They keyed in the wrong tax code or the P6/P9 process of acquiring a tax code from the HMRC electronically went wrong. This should be obvious though on your payslip.

4) They set you up as if you have another job. Using advice for RTI starting declaration 'C – they have another job or pension', you would be set up on 0T tax code and Week 1 Month 1 Basis (not cummulative tax as normal). Again I would expect this to come up on your payslip.

There's a ton of possible mistakes that could have happened really.

As other people have mentioned, yes, you will pay tax before you have actually earned enough to pass the basic allowance, as long as you look on target to pass it by the end of the year, that's normal.

NI is calculated based on pay period, weekly or monthly. NI is not cumulative, so each month will be calculated independently. Tax is normally cumulative (unless you are on a Week 1 Month 1 Basis, which sometimes people are put on when they first start a job), so it will take into account how much you have grossed, and how much tax you have paid so far this year.

If you have any trouble calculating any of the figures, send me a PM, and I will see if I can help. I work on a payroll software, and I know our figures are more accurate than those of listentotaxman or some other websites. I'm not a super expert, but I know a decent amount about payroll.