Sold a laptop and it’s gone wrong, help

England. I sold a laptop to a man this past Saturday and all was well. The laptop was spot on the whole time I owned it (3 years).

They messaged me on Monday morning to say that the laptop won’t turn on and that he wanted a refund.

I thought it was mighty strange and didn’t reply - I know this was wrong but in all honesty I had no idea what to say to that.

Fast forward to today and they have posted a bill / request for a refund of £545 through our mailbox on letter headed paper from their ‘solicitors’. I will not pay it, the laptop was fine when I sold it on Saturday.

What can I do as the are threatening to take me to court?