I believe that as a US citizen I can enter the UK or the EU (until 2021) without a visa for tourism or business purposes for up to 6 months. (Correct me if I'm wrong.)
I'm an independent consultant with clients in the USA. While traveling – for leisure! – I will from time to time also do work for these clients – not just checking email, but also writing/reviewing documents, programming, etc.
This is presumably allowed. (If not, why not?)
My question is: Do I need to mention any of this if I somehow get stopped on entrance and asked what the purpose of my visit is? I'd like to know if the one-word answer "tourism" is sufficient in this case.