I've never been to the Old Bailey but I've researched it and thinking of going soon. From what I understand, you can go see pretty much any trial from the public galleries but you might have to queue up - if it's anything like the public galleries in Parliament you'd be well advised to 45 minutes to an hour early at the very least, possibly more for mayor trials like Daniel Khalife's. You'll go through airport style security and you cannot take your phone with you to the galleries. The Old Bailey won't take care of your phone for you but apparently there's a newsagent nearby which rents out lockers or offers some other phone storing service for a small fee - very important to go deposit your phone there before going into the Old Bailey to not waste your time and potentially lose your place in the queue!