This happened to me. Not a lot of money so I refunded after about a week because I didn’t want to take a hit with the feedback and then started a claim with Royal mail once the 15 working days were up.
RM ask for a statement or completed form from the other party too as part of the reclaiming process but there is no incentive for them to play ball if they already have their money refunded so if you refund in advance, get them to write something first to state the item never arrived.
My other party didn’t bother for me. I got my money back from RM in the end (about a month later) but I had to be quite er assertive on the phone a couple of times.