Most aircraft noise is exempt from the statutory nuisance regime and aviation policy and regulation is largely controlled by the UK Government; principally through the Civil Aviation Authority (including in relation to heliports and helicopter flights). However, the CAA do not have the power to restrict aircraft activity because of noise nuisance. In some cases the local planning authority may have imposed restrictions on operation (again, they are based at your local authority).
There are restrictions on flights associated with the major airports; some of which are regulated by the EU. This is a particularly specialised area of law and acoustics and falls outside of the scope of this document.
Some airports offer insulation schemes and grants to mitigate against the effects of noise. You should contact the airport concerned directly for more information.
If you wish to make a complaint about aircraft noise you can complain to the airport concerned (where the aircraft is travelling to or from). You may also register a complaint with your local authority though as this will help them measure trends in interest and concern (even if their powers are limited in relation to noise nuisance).
Military aviation is controlled by the Ministry of Defence who can be contacted through the MoD Complaints and Enquiries Unit.
Further information on civil aviation can be found on the CAA site. Other useful websites include laanc.org.uk and airportwatch.org.uk.