Update: RAC (UK roadside breakdown service) turned up and switched it out in under 30 minutes, we found a wood screw in the tyre which is what caused the puncture.
I couldn't change it myself due to not having the tools with me. Luckily my boss understood and I actually got out of a call I didn't want to go to so silver lining I suppose.
Not trying to pile on advice that's not helpful in your current situation, but I would really recommend getting an air pump to keep in your vehicle at all times for precisely this situation. Mine has saved my ass several times just over the last few years. And that's also weird about your locking lug nuts—when I had a vehicle that had those, it came with the socket adapter included in the standard roadside kit.
The stock tire iron is usually trash, go to Harbor Freight (before you get a flat, unlike what I did) and get a 24" 1/2" drive breaker bar and whatever socket is needed for your lugs. With that, even if they were put on with an ugga dugga gun you can remove them with relative ease.
Also if you get one without a rubber grip it will last forever because it's just a big piece of metal.
They might not be able to if the tires are still factory and were put on with an air gun or they still have locknuts on them. I learned that one the hard way.
They make tire inflators that can be plugged into your car's DC outlet. In the event that your tire isn't thrashed, you can fill it up and keep on going. I had a slow leak in a tire for 9 months that I just topped off until I got it fixed. Sorry about your luck, friend.
A few years ago, I had the worst string of bad luck. My car was about to go down in flames so I bought a new one. These are just the car related mishaps. I bought a brand new car in October. In December someone ran a red light and hit me. Low speeds so just vehicle damage. A week after I got it back, a tire popped due to something on the road. THE NEXT DAY, a second tire popped for the same reason. Two weeks later, a third tire popped. This time they didn't have any in, so I had to wait without a car till it came in.
The guy came out to tell me, having been there through everything that happened, and the look on his face when I just started laughing was priceless. Remember this isn't all that happened during that time. It actually broke me that day, but in a good way. I don't really get angry or upset much anymore. But it actually scares me when my response to something bad is to laugh because of all that.
We had another string of bad things happening that ended last month. So much stuff broke at once. Second time I started laughing in reaction to bad news. Good times.
I feel you. I’m sitting in the shop right now for a sheet metal screw. Just got the news that they can’t repair so I’m buying a brand new tire to replace a tire that only has 800 miles on it (well, and a sheet metal screw).