Amex is widely, but not completely, accepted among big retailers. I find it unusual when a small or independent business tells me they accept it.
Several UK banks issue dual Amex/MC accounts so you use the Amex wherever you can, and switch it for the MC when you find a non-Amex location. So that tells you all you need to know about its acceptance. However, I mainly shop at big retailers and can go months and months without pulling out the Mastercard.