Jay - perhaps you haven't noticed but the security level in UK is SEVERE - that means a terrorist attack could occur at any time. You don't have to be a rocket scientist to realise that the Capital is a prime target - hence the police helicopter will be used for pretty much any event as both a deterrent and and immediate reaction platform for observation/communications.
You seem to be happy with having a police presence in London but just don't like the noise (frankly it is insignificant compared to the traffic noise) - perhaps you should understand it is about keeping you and yours safe and that it is actually a very good way to spend taxpayer's money.