The Radiocommunications Agency (now OFCOM) issued some guidance about this in 2001.
The specific offence is defined by s5 Wireless Telegraphy Act 1949:
Any person who ... uses any wireless telegraphy apparatus with intent to obtain information as to the contents, sender or addressee of any message (whether sent by means of wireless telegraphy or not) of which neither the person using the apparatus nor a person on whose behalf he is acting is an intended recipient ... shall be guilty of an offence under this Act.
It's also an offence under s5(1)(b)(ii) to disclose the contents of any such message, so the reception and disclosure of radio messages not sent by or addressed to you are both offences.
I don't know if there have been any successful prosecutions specifically for monitoring aircraft communications. I doubt whether a hobbyist listening for his own enjoyment would attract the attention of the authorities, but if he started to publish recordings of the traffic then that might well do it.