Ok, first of all, yes, a civilized country can declare colonial war on another civilized country. When engaging in that kind of war, only states that do not have "statehood" in your country will be eligible for invasion. (If you click on the list of states, the eligible ones will have their names greyed out.)
Second, to do so, I'm pretty sure you can't already be involved in another war. Holding your mouse over the blacked-out "declare colobial war" button ought to give you the reason you can't.
Third, just because you have all but one of the claims in a colony doesn't mean you can claim it. You either have to personally own all the claims--all of them. Or, you can one of each of the four types, and as long as all the other provinces have been filled up by someone--anyone, but they must have been filled by--then you can claim the whole thing.
PS. I wouldn't recommend a colonial war against the UK, though. It's probably a better idea to build up relations and trade them something for the claim, if you want it that badly.