Question on Commando...
In-laws turn out to have a commando socket I could use, but it's on a 13a fused spur (installed for weather proofing, not power capabilities).
Will I be OK using this with the car to limited to 13a and get a useful boost over a 3 pin charge?
If it's as you describe, then it's questionable. The reason the 13A plug adaptor is limited to 10A by the UMC is the heating effect from the fuse potentially causing long-term degradation. Here as I understand it you have the exact same 13A BS1362 fuse in a fused spur unit and then a Commando on the end of it - a somewhat unusual arrangement (especially as you say it's actually a radial circuit direct from the consumer unit). The only explanation I can come up with is if they ran out of ways in the CU and so this is actually a spur off a ring circuit as you originally said - just happens to be tapped off the 'root' of the ring rather than half way round.
There's two questions to answer : what is the safe maximum current to intentionally use, and what risks are there if you forget/the car resets itself to the full 16A?
Here's a link to some data on BS1362 fuses (just from google, not a site I have any connection to)
Why does a 13A fuse not blow at 13A?
You can see that the 13A fuse in that fused spur unit will not blow even with the car taking 16A - its job is to blow in the event of short circuits, not to police small overcurrents.
You are clearly safe at 10A - that's the same as plugging the UMC into a 13A socket, and this arrangement is probably better mechanically.
At 13A, everything is notionally within spec, but that fuse will be getting hot; the prospect of long term damage at that level is why the UMC limits to 10A, but if this is for occasional use and you are able to monitor the temperature (say after it's been charging for an hour and before you go to bed), then 13A is perhaps reasonable (personally, in a comparable situation, I used to charge at 12A just to give a bit more margin; on Model S that extra 2A gives a bit more than the expected 20% improvement in charge rate due to improved efficiency).
At 16A it will probably work unless something is already defective. Personally, I'd only do that deliberately if I was desperate and in a position to monitor it regularly - never overnight. But the risk if it happens accidentally is fairly low.