Meters or metres-Which is correct?

Some words Brits write differently than other English speakers, words like-METERS, CENTERS and some others, in which Brits switch around last 3 letters and make them into metRES, cenTRES..etc. My Y.A. spell checker tells me that these Brit written words are erroneous, how do British spell checkers work?..Which is correct way to write these words?