The Road Vehicles (Construction and Use) Regulations 1986 prohibit driving whilst using a hand-held mobile telephone. The offence is made out if the defendant is:
(a) driving a motor vehicle on a road; AND
(b) holding the phone in his hand; AND
(c) using it.
There is an exemption which allows the use of a hand-held phone for a genuine emergency call where it would be unsafe for a driver to stop driving to make the call.
The offence can only be committed on a road (rather than 'on a road or other public place') and therefore if you are in a McDonalds car park or similar then you would likely have a defence to using a mobile phone on a road.
The offence is subject to a £200 fixed penalty and 6 penalty points. If the matter is dealt with at court then the there is a fine of up to £1000 and 6 penalty points or discretionary disqualification of any length.