Astérix!
From googling, it looks like boiled lamb and lamb in mint sauce are actually separate typically British recipes.
I have never encountered boiled lamb or lamb in mint sauce.
English lamb is always roast; beef if tough is occasionally boiled.
Roast lamb with mint sauce and green vegetables is absolutely fine, and some French chefs have said so. Lamb fat is rather greasy and mint sauce (fresh mint leaves ground up with vinegr and a little sugar) cuts through it admirably.
As a separate aside, though, not that many restaurants in the UK in my experience are actually very good at it, in fact my one lunch experience at the Savoy was disappointing. It's very much domestic cooking, and the best roast lamb I ever had outside the home was a small family restaurant in Dijon.