I was recently made redundant from a role at a UK company. They were very reasonable about the situation and offered to pay off my 3-month notice period rather than make me work it.

As a result, I was lucky enough to get a big windfall: my wages this month were three times higher than normal - let's say it came to £10k (it didn't, but it's a nice round sum to use). I do not pay top-rate tax so I was expecting to pay tax on this at 20% and see £2k go to HMRC. It is possible this windfall will take me into the top-rate band later this financial year, but it has not so far.

However, according to my payslip, the actual figure I've paid is much higher, nearly £3k. To be clear this does not include National Insurance, which is listed separately.

I queried this with HR at my former employer and got this reply:

"You are able to earn a set amount each month which is tax-free (determined by your tax code). Anything you earn above this amount is taxed, therefore your tax this month would be greater because you’ve taken home essentially 3 times as much in 1 month.

For example, if you earned £2000 a month and your tax-free amount was £1000, you would pay £400 in tax (if you’re a higher rate taxpayer) – times this over three months and you pay £1200 in tax. However, if you earn the whole £6000 in one month, your tax-free amount is still £1000 and you end up paying £2400 in tax."

Now the calculation here is easy enough to follow. What I don't understand is how this applies to me because I've still paid tax on this at 30% rather than 20%.

Before I query this with HR or HMRC and make myself look stupid I thought I'd better check: am I right in thinking I have been over-taxed?