I've been visiting quite a few cigar shops, sampling lounges and terraces across London. You can find reviews of each one here:
https://londoncigarsmoker.com/cigar-bars-terraces-smoking-lounges/
This might help you find a place.
I also have some reviews from Edinburgh here:
https://londoncigarsmoker.com/cigar-bars-terraces-smoking-lounges-in-scotland/
If you go to Edinburgh they also have a Puffin Rooms there which is meant to be good - but I've not tried there yet.
From my opinion London is a better place to visit for cigar scene as there are a lot more places you can head too, well compared to Edinburgh.
Hope this helps and enjoy your visit to the UK 🙌