HMRC do sometimes send refunds without prompting
What they do is send you it in the form of an obsolete payment instrument known as a "cheque".
This happened to me about 5 years ago. A dodgy ex-employer didn't report my salary to HMRC or pay the tax on it, so they thought my other income which I paid basic rate tax on was covered by my personal allowance, when it wasn't, and refunded the tax I paid on it.
I wrote to them to say they had made a mistake, and they should probably ask for the money back. They ignored the letter. Which means I can now legally keep the money.
I've found that a lot of younger people have never seen a cheque before and don't know what to do with it. You have to take it to *your* bank, not necessarily the bank the cheque was drawn on, to pay it into your account. There are a few banks that let you pay in cheques by taking a photo of it with your phone "B" is one such bank that offers this.