All emitting devices whether installed or used in aircraft are required to be licensed in accordance with the provisions of Section 8(1) of The Wireless Telegraphy Act 2006
The only exemption to this law as regards cellphones is as stated in The Wireless Telegraphy (Mobile Communication Services on Aircraft) (Exemption) Regulations 2008. This basically allows 1800 Mhz cellphone use with on-board pico-cell systems above a heght of 3000m. The sort of thing which Ryanair has in some of its aircraft.
So the law you would be breaking would be a general law regarding licensing of emitting devices in aircraft, not one that specifically mentions cellphones. Whether public transport or private is nihil ad rem; your cellphone is not licensed for use in an aircraft.