Global taxonomy on multiple posttypes

Hi fellow WP’ers!

I’m on a lookout for a way to create a global taxonomy (tag) which can be used in multiple posttypes. Here’s what I was thinking:

1. I have 2 posttypes (example “Shops” and “Locations”)
2. I would like to have a global tag, covering both posttypes (example “London”)
3. When adding tags, I would like to have these tags included in the “autocomplete” on both posttypes

Is this possible in any way??
If not – is it possible to duplicate tags to other posttypes? If so, how?

I’ve tried a lot of different things – but I really can’t seem to find a solution.

Can someone help out – or at least point me in the right direction?

Best regards
Aris