You have to look at this in two aspects - firstly, how the media portrays politics, and secondly, how politics has adapted. In the long run both have changed dramatically, but not completely towards the USA.
The media has certainly started to see politics within the same light as it is seen in America, this is evident through the televised debates and advance of shows like question time. But the media is answering to a movement which has orginally derived from politicians themselves. Because of the rise of social media and technology we are seeing a massive movement towards New Socal Movements (NSMs) and certainly away from the old days of soapboxing and policy-first. Instead we are seeing a far more celebrity status to our politicians who now tweet their every move, blog, go onto TV and attract media attention with visits to charities, homes and the like. Is this from the USA?
yes and no. Yes in the sense that the USA have been doing this for years, well before the social media began to spread, and did this because the President is a big deal - he is the head of state and top representative for the very patriotic and nationalist country, so his image is a very important part of politics. On the other hand, Britain has been evolving for years with regards to the role and actions of representatives - So, the first true theory of politics in Britain was the Burkean theory, then the parliament theory and onto modern politics where it is far more important to look the part. Nevertheless, all this really started to come about when Margaret Thatcher came to power - She started a strong relationship with the USA and whether or not the two are connected, every prime minister since has pushed to try and look the part - changing the way they look and talk ect. Tony Blair is a big example of this.
Now in terms of politics, well this is a little more tricky. British Policies have, by no means reflected that of the USA, nor have we become a two part system where both parties are extremely right wing - will still have a little adversary politics. However, some of our social reforms and laws, especially those created by New Labour, have been very influenced by the USA - and many of the institutions and language used in politics are American in origin. Even the transformation of our police is one towards a more USA/European model.