We have a mixture of wiring systems for sockets, as said a BS 1363 device uses a BS 1362 fuse which has a maximum rating of 13 amp. Does not matter if a socket and plug or fuse connection unit. I don't really know why a double socket is permitted, the regulations say the cable must be rated 20 amp or more and be 2.5 mm² unless using mineral insulated cables or more.
I would assume the rule no un-fused spur from an un-fused is so you can see without testing if part of a ring final or not? As clearly a double socket can deliver the same power as two single sockets. However in real terms you do need to test it is a ring anyway, so seems strange, likely some historic reason I have never been told. But a un-fused spur can only feed one BS 1362 device be is a single socket, double socket, or fuse connection unit.
If it feeds a FCU then all after the FCU is fused, so then as many sockets as you like.
What seems unclear is how grid switch system fits in, as you can have two independent sockets in a double back plate, in a standard double socket box, I used these
to convert a double socket to a single socket, switch and fuse to then add more sockets to the spur, sorry poor picture, they are also handy to extend a ring final using two single sockets in a double face plate.
The ring final was developed near the end of WW2 to assist with the re-building and used 7/0.029 cable which was thicker than the 2.5 mm² used today, and there was no insulation on the live pins so heat could transfer better and be dissipated, so although designed so we could use electric fires to heat the home, in real terms not really suitable any more, so the IET has advised that any fixed appliance over 2 kW has a dedicated circuit, there is a weight limit to portable unless it has wheels, so if we followed this advice washing machines, tumble driers, dish washers, immersion heaters would all have a dedicated supply, however only the immersion heater traditionally has a dedicated supply.
Use of radials, both with 2.5 mm² and 4 mm² the latter often on a 32 amp supply means care needs to be taken, I remember an office block where clearly some electrician had not realised it was a radial had split the radial and inserted a loop of 2.5 mm² cable in the middle of a 4 mm² radial, not DIY as industrial premises with in house electricians, so this error was made by an electrician, cure was swap MCB from 32 to 20 amp, but not ideal.
We are told we should not change the current capacity of cable within a circuit, however this can't really be avoided, as when the cable changes installation method enroute that means a change in current carrying capacity.
It is a problem when one is asked to increase the supply, in theory the fuse/MCB/RCBO protects the cable, but when fitting some thing like a hob or oven, the hob or oven may have a maximum supply requirement over 13 amp but under 32 amp normally supplied and you can't get a 16 amp FCU, so only option is change the MCB to 16 amp, but when that is changed back to a unit wanting 32 amp, the electrician is faced with assessing if that cable is good enough to carry 32 amp, if he sees 6 mm² at cooker end and consumer unit end he assumes it is 6 mm² for whole run, but to assume is wrong.
Domestic premises have a lack of wiring diagrams and history recorded, even the installation certificate does not show the PSCC or loop impedance at centre of ring, or end of radial, so to ascertain if any cable has been added or removed is near impossible as simply no records.