Lets look at the scenario in action....
You board the aircraft, take your seat. Handling agent confirms everyone and their bags are on board. Paperwork is complete. Lovely, ready to go! However there were issues during turnaround that have delayed the flight slightly...
You.... quite clearly thinking of only yourself, your boarding an aircraft, not a bus.... decide you wish to offload before doors closed.
Handling agent has to change all figures, notify boarding team. Aircraft may be remote parked, bus may be required to return to aircraft to take you back. Taking up ramp staff and passenger services staff time, which with the weather situation at LGW would be valuable in other areas.
Pilots have to change their paperwork, doesn't take long, but an inconvenience when on a short turnaround.
Hand luggage and security issue has already been mentioned above.
And that is if the aircraft is near to on time BEFORE doors close.
Then you have to worry about de-icing, pushback delays, slot delays, taxiway/runway issues with recent snow...the list goes on.
If you think you might not make a connection in the first place, and know the airline you fly with wont cover you, don't book it!
If you still insist to risk it, at least decide before, or during boarding to offload yourself at the gate, much less hassle for everyone! And you wont look like a **** for walking off the aircraft after already getting on.