Who pays VAT on goods sold through a pop up shop

Hello,   I would be grateful for any help on this issue.

I sold goods at a a "pop up" store.  All incoming sales went through their till and I am receiving 100% of the sales.  The money has basically sat in their bank - they have not made any profit from it (they charged me a separate fee for the use of the store on which I paid VAT) How do we account for VAT on sales.  Do they receive a VAT invoice from me and they claim it back or do i issue a non VAT invoice but pay VAT on the sales from my end as normal.  I don't want to pay VAT twice or not pay at all.  Bit confused.  Any help gratefully received.  Thank you!