Er, that's a definite 'No' and a possible 'Yes' ;-)
Section 41d of the Road Traffic Act 1988 (as amended by the Road Safety Act 2006) makes it a specific offence for drivers of motor vehicles (only) to use a hand-held mobile phone while driving. This section of the RTA 1988 does not apply to cyclists.
However, prior to 2006, several motorists were successfully prosecuted for 'driving without due care and attention' because they'd used hand-held mobile phones while driving.
Section 29 of the RTA 1988 makes if an offence to cycle on a road without due care and attention. So, although it's not a specific offence to use a mobile phone while cycling, a prosecution might still be possible anyway (under the due care and attention' rules).
Chris