Indeed, that would seem to fit with what you've described. To be sure, you ought to find that one of those latter sockets (the last one in the line) will have only one cable going to it. The 'radial type lashup' would normally be described as an (unfused) spur - perfectly acceptable, safe and and compliant with regs if it supplied only one socket (which clearly in not the case!)
I've checked the sockets in question and they have two wires going to them so I can't find the end of the unfused spur.
I'd hazard a guess that the builder thought he had extended the ring (hence he ran two new cables from the same room to the extension) but got it wrong. Maybe there's JB under the floor in bedroom 2 somewhere and the actual topology is two rings connected by a spur; dumbell shape if you like, who knows. That would at least explain why the affected sockets have two cables each though. I'll know for sure once I have physical access and will keep the circuit de-energised until then.
I don't want to fuse down and I agree that the easiest way would be to rectify the situation is as you said; establish the path of the cables though the affected sockets, break the existing ring, incorporate the affected sockets spur into the ring and then test for continuity, bridges, IR etc.
The radial circuit idea had crossed my mind too as for a few reasons -
o After this experience, I'm not a big fan of RF circuits
o I don't like the fact that the whole house except the kitchen is on one ring and the area total area served by the ring may well be approaching the limit.
o I'm in a pretty rare position to conduct improvement or remedial works with minimal disruption - some carpets already gone etc.
o There is sufficient access to cables to split the house ring into three radials of approximately equal size (# of sockets). The diagram doesn't show the whole story as all downstairs sockets are run via vertical drops from the upstairs ones.
o If the circuits were split into three radials in this manner then I don't think the 20A per-circuit limit would be a problem due to the likely nature of the loads on the circuits.
The CU would benefit from replacement (no RCD protection) and has no spare slots so I can't add a circuit - which I believe would be notifiable work anyway - without replacing the CU, which I'm sure would be notifiable(!). I'm considering having this done for the reasons stated - it seems to make sense and would probably be cheaper and be less hassle to do now.
Now I've found this issue, and having previously found and rectified another which was quite serious (no main equipotential bonding to the gas pipe), I think the whole installation could do with a check-up anyway.
I'm not sure if my electrician mate is a member of a self-certification scheme so, even if we conducted the CU replacement and testing together, I'm not sure that he could sign it off (not really sure how the legislation works in this regard). I'll have a chat with him about the options when he's here. I'd be nice to keep the costs down while still doing a proper job of course.