Fuji, not that I work for the CAA but maybe I can help. There does not appear to be anything in the ANO or Rules of the Air specifically prohibiting the use of mobile phones in aircraft. AOC holders may need to put something in their Ops Manuals an the topic in order to get their certificate but I don't think there's anything similar or GA operations.
I don't know - any more than the CAA bod does - what restrictions the contract which someone else has with their telephone supplier...heck, I'm not even sure what my own one says! But if I cared enough, or thought it mattered in any particular situation, I would look it up. Just as anyone else should. And I wouldn't expect someone from the CAA to do for me - and I wouldn't want them to either...not at the rates they charge.
As you say, Ofcom or the phone service supplier are the best people to ask.
Going back to the ANO, there are many things that are either foolish or can go wrong when associated with aircraft. The rules don't cover everything. If you do something out and out stupid, the CAA has a general, 'catch-all' bit of legislation to prosecute people for endagering others. It's articles 73 and 74 for anyone who can't be bothered to do the research for themselves!