The following is just information which may prove useful down the line. I hope its as simple as a bad earth connection though !!
Since the ignition switch turns on most of the circuits required for running the engine (either directly or via relays), the fact that the lights flicker when the key is wobbled about would suggest that this is the place to look first.
I'm guessing since you are based in Wales, that you have the HISS system ? This is not likely to be a problem. While a fault in the HISS may cause problems starting, once started, the engine continues to run without the chipped keyfob being present. HISS only needs the chip in order to start the engine.
I have absolutely no experience of repairing or replacing faulty ignition keys on the 1300, so I can't help there I'm afraid. But I can surmise from looking at the microfiches (I use Lings Honda for this). There are 3 main parts to the ignition key - the locking barrel into which the key fits. On top of that is the receiver to detect the presence of the HISS chip in the key handle; and underneath is the base unit which performs the electrical switching.
You are unlikely to need the receiver.
If you decide that you need a new switch base unit - the part number is 35101-MCS-G01, and seems to be the same unit for models from 2002 to 2014 in the UK - so getting a second hand one from a breakers yard from a newer model should be no problem.
The switch mechanism is terminated with a 6 pin connector, which must plug into the wiring harness.
If it is the electrical switch in the base unit that is the problem, then your existing ignition keys and chip will still work. If you end up replacing the barrel, then you will need a key that is cut to go with it. It is possible to remove the chip from your old key and put it in the head of a new Honda style key. For testing, the chip doesn't need to be integrated with the key - the bike will start with a valid chip placed alongside the head of a non-chipped key, and the engine will continue to run after the chip is put in your pocket - until the ignition key or the red kill switch is turned off.