Do women ask men out in Great Britain?

No, its against the law there.

i think that can happen anywheres

As someone who is over 50, I can say that no woman over probably 40 odd would ever ask a guy out.

That said, my friend's daughter who is 20, has asked guys out and says that its quite common these days amongst younger people

No, they believe it is the mans job, like every other western country in the world.

not so much in my experience . . .