Sure it does, if and only if we're talking about lands that are in the temperate zone (amenable to those from the British Isles) and that don't have heavy indigenous populations to begin with. In such a setting, like in North America, Australia, New Zealand, and an ATL British Argentina, it would be easy for British settlers to move there and for British institutions and laws (which are generally superior to their Continental European counterparts) to take full effect. (A partial exception might be the plantation-based economy of the US South until relatively recently.)

Other areas that the British colonized in, like India and much of Africa, are in the tropics and already have had large (and relatively advanced) indigenous populations, and British colonization there takes a very different form which is not amenable to early industrialization. The Anglophone Caribbean is an interesting case, because while it's a) not as developed as North America, W. Europe, Australia/NZ, etc., b) there were plantation economies, c) most of the people there are descended from African slaves, d) in the tropics, the folks there are much more devoted to the British ideal than the rank-and-file in India or ex-British Africa and are generally much better educated.