Firstly, there are more than 'two' accents involved here.There are very many widely differing accents in the British Isles, and a number of different accents among US English speakers. There are in fact far greater differences within these two countries than between them. For example, if you heard an American university professor from Harvard or Yale talking to a British university professor from Oxford or Cambridge, there would not be an enormous difference between the way that these two people speak. However, if you compared the speech of the British academic, speaking standard Received Pronunciation, to that of a window-cleaner on the streets of Liverpool, Newcastle, Belfast or Glasgow, you would think that these people were speaking different languages. There is no such thing as a 'pure' accent. No accent is any purer than any other. Perhaps your teacher likes Irish accents, or find them easy to understand. And there are, of course, several fairly different accents within Ireland. As for the Queen, her accent is no longer really representative of how people speak in the UK. There are few people left who use the same pronunciation as the Queen. If you listen to the more relaxed pronunciation of her grandson Prince William, for example, you will get an idea of the more modern version of 'the Queen's English'. If you want to hear some clear, well-spoken RP (Received Pronunciation), look on the internet for British broadcasters such as Jeremy Paxman or Fiona Bruce, for example. Or Joanna Lumley - she has a a lovely voice.

The Irish accent the purest accent? Only the Irish would agree with that. :-) The Queen's accent has changed over the decades. You may find this article of interest. http://news.bbc.co.uk/2/hi/science/nature/1080228.stm

Is your teacher Irish? :) I think you mean "the Queen's English", by which we mean "proper, educated UK English". That would be an RP accent. Yes, the differences in accents (and accents between smaller regions of the US, UK and any English-speaking country) are obvious to us.