The traditional pronunciation was CONtroversy, with the stress on the first syllable, but more of us Britons are now saying ConTROversy, according to British Library research. The pronunciation of other words has changed -- schedule is now often pronounced 'skedule' and patriotic pronounced 'pay-triotic'. Those two changes are in line with American pronunciation, but what is interesting about the 'controversy' shift is that ConTROversy is not the American pronunciation, so the change has nothing to do with copying an American accent.
Other words have resolutely maintained their British pronunciation -- Britons are showing no interest in pronouncing attitude the American way ('attitood', instead of 'attityude') and are sticking to 'garridge' (garage) rather than the American 'garaahge'. Despite the Gershwin song (You say 'eether' and I say 'eye-ther') there is no Atlantic split between the two pronunciations, with both pronunciations being popular in the US and the UK. 'Scone' is interesting; almost all Americans pronounce it to rhyme with 'bone', but there are two pronunciations in the UK -- to rhyme with 'bone' and to rhyme with 'gone' -- and, as I said in this post, we can get very excited about which is the correct version.
For more on this story see this Daily Telegraph article.