I doubt very much that you would be allowed to visit the flight deck of a British registered aircraft in flight by simply asking as a travelling passenger. I also suspect that writing to an airline saying how interested you are in aviation and how you would be willing to undergo any necessary security checks would quite frankly be a complete waste of time.
May I suggest that the next time you fly as a passenger, perhaps after arrival at the destination, wait behind until everyone else has left then casually saunter forward and ask to "have a quick look". This would be the best time and may allow you some minutes to chat to the crew about what the job entails.