Not really, I know that Gordon Brown is the British prime minister who is opposed by David Cameron. Tony Blair is the ex. prime minister who had a long and largely successful tenure of which the low point is the Iraqi war and the high point is his part in the solution of the entire Irish problem.
The head of state is Queen Elizabeth whos role is largely ceremonial although she does have certain powers that she never uses. The two main parties in British politics are the Conservatives (Tories) and the Labour party.

I'm from New Zealand btw.