Made redundant, but bonus paid in oversight

The short version....

I was made redundant last year, literally the day the consultation finished and it was all finalised was Xmas Eve (yes, I was such a good girl that Santa took my job, but he did bring me a nice new shiny one in January !)

Anyway, having been there just over 3 years, I was entitled to a statutory pay out, a top up as specified in my contract, money for holiday accrued but not taken and money in lieu of notice. And a bonus payment. That arrived in my bank account in January, but no sign of a payslip in the post.

So I emailed the HR contact and asked her to chase it.

Exactly one month later (February), a mysterious payment from the old job with a tax code of 0T/1 appears in my bank account - I contact the HR dept at my old place and ask them to look into it, oh, and my final payslip still has not arrived. Friday of that week, two payslips arrive - one detailing what I had received in January, and February's mystery money, and one dated March, with more mystery money listed in it. I check my bank account and yes, that money, minus tax & national insurance is there.

So, I assume it's legit, based on having payslips, mutter a little because I think I've been over taxed, but decide to wait until after the weekend to do anything and start dreaming of a week or more in the sun.

Last week, the HR person emails and says that they overpaid and issued the bonus by mistake and they want it back. My response is that is fine, but I can only pay back what I received as HMRC took their cut. They said I should receive a letter from the old place's Payroll team, but I'm still waiting for that to arrive...

So - my question is twofold, what does tax code 0T /1 mean, and who is should be chasing HMRC, is it them, because they made the mistake, or me, because the tax/NI was taken from me?

My feeling is that it is their mistake to resolve, but I may be wrong...