I do refer everyone to Ed's disclaimer on this particular topic
Disclaimer: All Answers found here should not be taken in the stead of legal advice from a solicitor. Please also refrain from being rude, abusive or judgemental - users come here for advice, not judgement.
Nevertheless, stevie - the others are right. The airport and the flight paths were there presumably before you bought the house. Were you not notified? If there were something new, which was affecting a large group of residents, then there might be group petitions etc - but the fact that you are disturbed (and you don't mention any of your neighbours) suggests that it's you rather than an environmental issue affecting the neighbourhood. If it was there before you moved in, then you don't have a chance, IMO. Others seem to enjoy the traffic from these posts, I've lived near Gatwick and it didn't bother me.
We're not being negative or unsympathic - you asked the question, and most of us are saying that the answer to your question is No.