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Yep - in reality it's the number/code of the HMRC (tax authority) form you get when you leave a job.

Thanks... so kind of like how we would say 'pink slip' in the US.

A P45 is the official document you receive when you leave employment (fired or not), it isn’t slang for anything though you may be threatened with a P45

"The term is used in British slang as a metonym for termination of employment." [1]

[1] https://en.wikipedia.org/wiki/P45_(tax)

You seem to be telling someone who lives in London how British slang is used because you read about it a few minutes before on Wikipedia.

Fellow Brit here. Born, bred and then f'd off elsewhere. I'd argue P45 is slang for being fired.

Its slang because P45 has nothing directly to do with being fired. It is a tax document related to changing employment.

Something to do with acquiring a P45 as a noun, yes. P45 isn't itself a verb that means firing as I infer the OP to be saying.

I agree (born and live in London). I've never heard P45 used as slang, maybe you could use "given a P45" to suggest someone was fired though.