Other than some occasional small restaurants/pubs, and a few small indie shops, its basically accepted everywhere here in Edinburgh, I have a corporate amex and use it for expensing business dinners very often, and supplies from office shops, supermarkets, etc..
I used to have a corporate Amex, and it was a nightmare to use it in London. Even in places that said they accepted it, when I attempted to pay the card reader rejected it. That was about 5 years ago, maybe times have changed - it would be great to see data rather than a mixture of anecdotes.
Yeah, my success rate for the corporate Amex in Europe is 70-80% which means the remaining time I need to fill out more tedious paperwork to get reimbursed to my personal card. The US based finance team continue to insist its much better now, but a 20-30% failure rate is too high