Yeah, imagine the outcry if they made a movie about an American superhero like Batman and the entire cast was British except for Katie Holmes and Morgan Freeman! Oh, wait...
Fine, to be completely accurate the cast of Batman Begins is mostly from the UK... "British" excludes Cillian Murphy and Liam Neeson. But anyway.
It's a tricky thing, adapting a work from another medium into a movie - it's entirely possible to keep all the wrong parts and lose the important ones, we can all cite examples of that.
But I can't see how being blond and British would have made any significant difference to the Constantine character. Maybe it mattered in some way in the comic, but it didn't matter at all to the story the movie was telling.
Besides, it was Keanu's signing on to the movie that got it greenlit, it wouldn't have existed without him. Watching Keanu walk around with bleached hair would have been a major distraction, and his attempt at a British accent in Coppola's Dracula is still being talked about so it was a good call that he didn't try that again.