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surely it was on them to have paid Tax on my salary?
Not if they weren't expecting your total to exceed your allowance. What was the period for that £1285? Five weeks or more and you'd have had no PAYE liability on that pay rate.
Anyway, I'm guessing HMRC have done the calculation properly, they can collect it by changing your code for such a small amount, but it's probably easier to just send them the £50
Just got letter from hmrc saying I owe them £50. I changed jobs mid April 2022, the top line here is last payment from my old job, surely it was on them to have paid Tax on my salary?