It appears I misinterpreted some tax rules (pretty easily done as in a rush and moving house at the same time) and have overpaid tax that I didn’t need to.

Anyone else had to claim back due to their own mistake? What is the process, was it painful and how long did it take?

https://www.gov.uk/self-assessment-tax-returns/corrections

Yes, many times! I regularly forget to divide pension contributions by 0.8 and end up writing asking for my money back. They always oblige!

I phoned them up for this. They told me to just go in and update my online SA thing. A week or so later I received a cheque (albeit for not very much money).

divide pension contributions by 0.8? How come? I stupidly used the number on my P60 when I was supposed to deduct the pre tax contributions to pension which makes quite a difference.

How long did they take when you claimed back?

As simple as a letter? No forms / ID in triplicate posting passwords in the mail etc…?