From https://customerservice.starbucks.co.uk/app/answers/detail/a_id/3854/kw/Filter

Any customer who purchases a Filter Coffee to stay in one of our participating stores in the UK or Ireland, can enjoy a free Tall refill on us.

Customers must retain their mug and provide this to the barista when redeeming their refill. Once you leave the store, your visit has ended and any subsequent coffee refill thereafter would be considered a new purchase.

I just learnt about this a few days ago.