You might struggle to get 4 x 2.5 mm² conductors into an ordinary 13 A socket - the BS specifies min 8 mm² , but some manufacturer's terminals will accept 12 mm² (which is quite handy if you want to branch a radial).

Fig 15A does not preclude multiple spurs from one point, but they must feed only one socket, so daisy chains are out unless you start with 4 mm².

I suspect that most sockets nowadays feed very little - table lamps, computers, screens, phones, etc., but we still must allow for that 3 kW heater on a cold day.

one manufacturer's product I noted specifies max. of 3 of 2.5mm conductors .

A 2.5mm2 spur using T&E cable, where the cable is rated at between 13.5 and 27 Amps as per Table 4D5, is affected primarily by the installation method. If two double 13 Amp sockets are connected onto a single unfused spur then at best two 13 Amp loads will cause no problems to the supply cable. (Ref. method C). But ref. method 103# would not be a suitable means of installation and may cause cable overheating. Of course these days many appliances are rated at 2kW rather than 3kW.

2.5mm2 copper wire if used as a fuse link, is rated at about 80 Amps. But obviously the P.V.C. insulation is the weak link here. So after a length of time in overload conditions the P.V.C. may soften and cause problems.

If the two double sockets are only ever to be used for small appliances like a 100 Watt aquarium heater and a couple of air pumps then all is well. But that can not be guaranteed to be the case in a home where just anything could be plugged in. And, what about future use if the house is sold?

Z.