The US word that I had to be most careful of in the UK was "bum".
The US phrase "on the bum" simply means not be feeling well or if it refers to machinery or equipment means not working properly. A " bum" means a vagrant or hobo, "bumming around" means aimlessness, to "bum a ride" means to hitch-hike or ask for transportation from a friend, "bum steer" means bad advise. None of these terms would cause a blush in polite company but would be considered as casual usages,
The use of " UK" is far more common usage these days than 30 or 40 years ago. But when it was not so well known there was a joke about a US executive that had a British secretary. In answering a telephone call the secretary stated that the executive was not in - - that he had gone to the United Kingdom. After a long pause the caller asked if it was too late to send flowers for the services.
In my several trip to the UK I was always careful not to take any striped ties. I had no idea about whom I might offend by wearing the St. Bartholomew's Sons of Destitute Civil Servants Soccer and Library League pattern.