In general, if you have a complaint about aircraft noise, you should direct to it the airport where you think the aircraft was operating from. They have a duty to investigate your complaint and respond to you. Often, unusually loud noise can be a result of a flight not operating as planned: the airport may be able to tell you if that was the case, and why.
Decisions around when an airport is allowed to be open for flights, whether aircraft can operate at night, and how many aircraft are allowed to fly on any given day are often set out as part of the planning process approving the airport’s construction or expansion. In most cases, this process is run by the local authority where the airport is located. They may be able to provide more information about the conditions imposed on it.
For Heathrow, Gatwick and Stansted Airports, decisions such as these are overseen by the Department for Transport.
Military aircraft are covered by different rules to civil ones. If you wish to complain about military aircraft noise you need to contact the Ministry of Defence (MOD).
Aircraft noise is not currently a statutory nuisance in the UK. It is not covered by the Environmental Protection Act 1990 or the Noise Act 1996. This means that local authorities do not have the legal power to take action on matters of aircraft noise, and nor does the CAA have the legal power to prevent aircraft flying over a particular location or at a particular time for environmental reasons.