Let me present myself.
I’m a UK electrician, I have all my wiring regulations certificates.
Running spurs -
When you add additional sockets to any system, even if the rest of it is not part of any work you have done, the installer must take responsibility for the circuit right back to, and possibly including the supply box.(the supply box might already be up to its limits and an electrician would be expected to be able to work that out for themselves - thus a higher cpacity supply box might be needed-unlikely but possible)
This is because you are expected to assess the job and survey it properly before you start.
The OP is looking at what is considered good practice according to a Approved Code of Practice
Although this ACOP is known as the 16th Edition Wiring Regulations, the word regulation implies statutory law and is misleading.
The true regulations come under other legal instruments but these are very general things, whereas the ACOP is actually a from of good practice and much more specific.
Now the ACOP here(16th wiring regs) states that you have to run radials in a certain manner, but actually it isn’t true, you can run circuit any way you choose as long as the circuits comply with the law (such as Electricity at Work regulations, or Health and Safety at work act 1974)
Its entirely possible to comply with the law, without actually complying with the ACOP, however, non-compliance with ACOP can used as evidence of a lack of due care if you are prosecuted for failure to comply with the law.(ACOP have a quasi legal status)
Sorry about all that, now I’ll get to the point.
If you comply with the ACOP, you will almost certainly comply with the law, and the ACOP sets out its rules for installing radials and ring main systems.
Contractors prefer to have a set of simple golden practice rules to work to, rather than completely reassess and recalculate cable sizes and earth impedances for every single job, which in the end would only save a few pence in materials but cost a great deal in design time.
Your problem with a radial circuit could be(but not necessarily) this.
The ACOP allows you to calculate wire sizes and in a ring main, its possible to get away with using 1.5mm cable(even 1mm cable is possible sometimes according to the calculations), very few if any contractors would actually do this, they would almost certainly use 2.5mm cable, or even more in some circumstances.
If you ran a radial socket on 1.5mm cable, you would very likely contravene both ACOP and the law, because the earth resistance would be such that you probably could not achieve a low enough resistance to force protective devices like fuses to trip, operate or blow fast enough to protect the system in the event of a worst possible fault.So what I’m saying here is that 2.5mm cable for radials is a minimum in the real world.
You have to choose your protective device according to the time it takes to disconnect a faulty circuit and you must disconnect within certain time limits.
The system might well be designed and safe to run on rewirable fuses, but add a radial and you may end up needing to use sand filled cartridge fuses or circuit breakers(MCBs)
You would probably be ok with 2.5mm cable for a single radial, but add any more radial sockets after that and the earth resistances rise.
There’s also human nature to consider, few folks would actually take the trouble to survey the circuit properly, and work out exactly if there have been any previous alterations, which might mean you were adding a radial socket, onto another radial socket and so on.
The idea that maybe a socket has two sets of wires going to it, therefore it must be part of a ring main is misguided and could be dangerous.
You can run lots of radials if you want, but then you have to arrange protection devices, and you could do this by using a fused spur, as the 40 or 60amp fuse in the supply box may well not be good enough protection.
There is hardly any need to run a radial anyway, all you do is decide where you intend to break into the ring, which will be at some particular socket, you disconnect one set of wires from that socket, and instead you run another set of wires from it up to your new socket, and you then return back down from the new socket and put the disconnected wire and the return into either another socket next to the break in point, or you use a junction box.