Good news - I found the problem and have fixed it. The problem was the PL259 connector that attaches to the back of the radio. Whoever fitted that connector messed up as there was a direct connection between the shielding and inner core. I resoldered a new one and received a 5 out of 5 radio check. The reception was also noticeably louder and clearer.
You may well ask why I didn't realise this earlier (since that was my original suspicion), and that would be a good question. It all stems back to my original incorrect assumption that there should be NO electrical connection between the shielding and the core. This came from a video demonstrating how to solder a new PL259 connector, suggesting you should test your work by using the continuity test on the multimeter to check for an open circuit between the centre pin and the outside of the connector. Obviously, that person was testing a cable that wasn't connected to an antenna. Now that I know about the loading coil, I should have instead been measuring the resistance. When
I cut the suspect connector off the cable I made the real error - instead of retesting the plug, I repeated the continuity test on the exposed wire. Because it returned the same result I assumed the plug was not the problem, and that another issue existed somewhere up the cable.
With the better understanding I know have (thanks to you all), I now see that measuring the resistance in the first place would have revealed that yes there was a problem, and re-measuring it on either the severed plug or the exposed cable would have identified the problem immediately. I am very sorry it took so long to reach this conclusion and am extremely grateful for all of the suggestions offered above. As well as fixing the problem, I have learned a lot in the last couple of days!