Blunkett agreed that the UK would extradite Britons to the US in future, without any need to produce prima facie evidence that they are guilty of anything. But the US refused to do the same with their own citizens. The Home Office press release concealed this fact - out of shame, presumably. Why did the US refuse? According to the Home Office, the fourth amendment of the US constitution says citizens of US states cannot be arrested without "probable cause". The irony appears to have been lost on David Blunkett, as he gave away yet more of Britain's sovereignty. If we really were the 51st state, as anti-Americans imply, we would probably have more protection against Washington than we do today.
So the US and Britain seem to be more like China and Hong Kong; i.e., one country with two systems. Real power rests in Washington, while Britain has sufficient autonomy to offer its nationals different lifestyle choices (gun control, nationalised healthcare, no capital punishment) within its territory.