This has been a problem for years, the standard 16 amp fuse
is larger than the 13 amp fuse, so it will not fit in a standard FCU, it would be good if you could have a German socket
and a 16 amp fuse next to it, so we can use appliances designed for Germany, however in real terms a 13 amp fuse will for a short time take over 13 amp, and likely any appliance rated 3.5 kW would not rupture the fuse as not used for long enough.
The rating for a double socket seems to depend on make and type, filtered sockets and sockets with other extras are often rated at 13 amp for the pair, many are rated at 20 amp for the pair, seems it is considered we would not use two 13 amp appliances together, they have not seen my kitchen, with two cup boilers together, ready for the coffee making in the adverts.
The problem is when we moved from 7/0.029 cable to 2.5 mm² cable we dropped from around 2.9 mm² and at the same time went up to 32 amp instead of 30 amp, plus other mods through the years like reducing the live pin size at top and covering with plastic to stop finger contact, which also reduces the heat the pin can dissipate, so running an immersion heater from a 13 amp socket is not recommended due to the time it draws the 13 amp for.
So we can over load the ring final at the ends, as the current is not equal shared, the cable needs to be rated 20 amp, and be 2.5 mm² unless mineral insulated where 1.5 mm² is allowed, but the whole system works on near enough engineering, and we are told any non portable appliance should have a dedicated supply if over 2 kW, so with oven, washing machine, tumble drier, dish washer, immersion heater all with dedicated supplies it is unlikely the ring final will be over loaded, my leaf blower is about the only item I have which is portable and could be used for an extended time over the 2 kW limit.
Yes I know we only seem to put the immersion heater on a dedicated supply, however since in theory at least the oven is over 2 kW and too heavy to be classed as portable, to produce a fused outlet for the oven would be against the BS 7671 recommendations in the appendix. So we don't have them.
Although we could say there is a chance of over load on the ring final, experience shows us this is very rare, the 32 amp supply in the main with a domestic property with the limit of 106 meters of cable in the main works well, and more to the point is cheap, with radials to each socket and 16 amp RCBO's on each radial even if some sockets doubled up, likely looking at 6 to 20 radials per house compared with 1 to 3 ring finals. At around £20 each the cost of RCBO's plus the cost of cable, would add a lot to the wiring bill. It need three radials to replace one ring final, and once you have more than 1 socket you have to consider over load tripping as well as volt drop on the cable.
So yes there are faults with the ring final system, but the plus points are greater than the minus, I does seem there is a move from the ring final, even the simple socket tester with loop, the lowest reading is around 1.7Ω to 1.9Ω depending on make, and pass mark is 1.38Ω, so clearly really made for 16 or 20 amp supplies not our 32 amp supply.
But it has worked well since the second world war, so see no reason to change now.