Not just in Britain. When I was working at Wagz I saw many obese dogs. Some people said they tried to help their dogs lose weight, while others denied their dog was overweight and others blamed their spouses for giving all the treats. Most people can't stick to a routine because they feel sorry for their dog and "think" it's starving or is finicky (from the extra fat stores) and won't eat so they give the dog whatever it wants so it will eat. Nature didn't intend it to be this way. I know it can be done. I've had Jake (shitzu)for 2yrs now. He is on thyroid medication. He just turned 10. He was 30pds - now he is 15pds. From any records I have he's been obese probably since he was 2 1/2yrs old. The incredible thing is half his tail was huge. Could barely circle it with thumb and finger.
It's like he has a new lease on life.
He still looks bulky because he has a large frame for a small dog. He's short legged, long body and large rib cage. It was 3 months before he could go up 3 stairs. His teeth were disgusting but he had to wait for some weight loss before having 18 teeth pulled which has also contributed to a happier/bouncy/loving little dog.

Just as a side note: Care needs to be taken when putting a dog on a diet. Many dogs have thyroid issues these days that also needs to be addressed first. Personally I'm not big on senior/diet/reduced calorie dog or cat foods. I however prefer a raw diet (full of nutrients) but less fed.