Here's the British answer : 'No'. And 'Yes'.
In Received Pronunciation they are different : 'aunt' is pronounced with a long 'a' as in 'father', while 'ant' has a short vowel as in 'fat'. In Received Pronunciation, 'aunt' rhymes with 'can't', while 'ant' rhymes with 'rant'.
This means that if you are learning British English you will be taught to pronounce these words differently.
However, it would be very misleading - not to say wrong - to make the statement 'ant and aunt have different pronunciations in Britain'. This isn't true. It all depends on the region. In the south of England these two words are pronounced differently, but most people in the north of England (Manchester Liverpool, Newcastle, for example) pronounce them the same. Also in most Scottish accents. Then there's the Wales and Northern Ireland, and many other regional accents besides.
Or in other words, there are tens of millions of people in Britain for whom 'ant' and 'aunt' have exactly the same sound.