I hoped the use of GBP in the OP made it clear where I would be selling, my bad.
It made clear where you were, not where you would be selling. I'm in the US; I could ship to any country. So could you. And you could run your auction on the US Ebay platform and specify you will ship only to those in the UK, for example.
Fact is, you're correct. Ebay UK requires sellers to have a PayPal account. You either have to get one of your own as a personal account, get one as a business account, or use the account of someone else.