As this is a regular topic for discussion, the relevant information from the UK authorities is detailed here.
The full text can be found at the following site (OFCOM) in PDF format.
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.
And OFCOM also gave PPRuNe the following direct interpretation of the law (similar to the above).
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.
In practical terms, you are unlikely to be prosecuted for simply listening in, if discrete and sensible. However, if you pass on information from what you hear, through Bulletin Boards, the press, or by setting up a live feed, then it's entirely feasible to feel Ofcom's hand on your collar and an appointment before the beak.