Get yourself a Yupiteru MVT-7100, an excellent piece of kit which will enable you to listen to anything from analogue cordless home telephones to VHF and UHF airband. The official law is as follows:
Anyone who intends to listen to radio transmissions should be aware of the following:
A licence is not required for a radio receiver as long as it is not capable of transmission as well (The Wireless Telegraphy Apparatus (Receivers) (Exemption) Regulations 1989 (SI 1989 No 123). The exception to this is that it is an offence to listen to unlicensed broadcasters (pirates) without a licence. Licences are not issued for this purpose.
Although it is not illegal to sell, buy or own a scanning or other receiver in the UK, it must only be used to listen to transmissions meant for GENERAL RECEPTION. The services that you can listen to include Amateur and Citizens' Band transmissions, licensed broadcast radio, and weather and navigation broadcasts.
It is an offence to listen to any other radio services unless you are authorised by a designated person to do so.
Which means....
In short you can use a scanner to listen to anything broadcast for general reception, radio amateurs, CB, weather and navigation broadcasts. Unless you are a police officer or work in the emergency services you are not allowed to listen to their communications.
You can only listen to other services if you have the permission of the sender. The air show is a good example where the control tower frequencies are publicised and that would be considered permission.
You can find out more about the law here -
http://www.ofcom.org.uk/static/archive/ra/publication/ra_info/ra169r7.pdf
But...who's ever going to know
Here's some Air Traffic Control frequencies (MHz) for you, you must have permission to listen to them though:
119.775 - London Control - London TMA Northwest Departures
118.825 - London Control - London TMA Northeast Departures
119.775 - Heathrow Director - Heathrow Approach (north stacks)
120.4 - Heathrow Director - Heathrow final approach director
123.9 - London Control - London TMA inbounds, Lambourne sector
120.625 - Essex Radar - Approach for Stansted and Luton
That's only a few of them, you might even hear me on some