Does make it harder for you, if you did sign something then you case is weaker but firing you for such a minor thing over 5 years service does smack of idiotic management. Had you been warned or disiplined before? Unless you accepted gross misconduct then you should have had at least 5 weeks notice (or pay in leiu of notice), I would go to your CAB anyway, as you could make a claim for unlawful dismissal anyway.
Yeah, go to the CAB. I'm not really sure why you thought we'd be more help than them - that's the thing to do and any Google search would have told you that if you didn't already know! As you've been working there over three months, I would look at unfair dismissal. Take a copy of your contract (and employee's handbook if you have a copy) to the CAB with you. You're most likely not going to get your job back. You need two verbal warnings and one written before you can be fired, unless it is for gross misconduct. Your contract or employee's handbook would explain whether it was listed as gross misconduct. Strange, but it could happen (gross misconduct is usually violence or theft). As said before, if your job has some kind of sensitive areas or information, they can legitimately request you don't take a phone - if it would interfere with equipment or you have industrial secrets that they wouldn't want copied. Other than that, I would have thought it would just count as a warning.