I wouldn't be surpised to find that The Queen actually received the most votes for best British film as well. It would seem logical for the rules to provide that the winner of the more prestigious category become ineligible for the lesser.

Crouching Tiger, Hidden Dragon won the US Academy Award in 2000 for best foreign-language film, but it had also been nominated for best picture. Had it won best picture, I'm sure the foreign-language award would have gone to the second-place finisher.