The RFC (Ring Final Circuit) to give it it's proper name did in fact save on cable compared to radial circuits at the time.
Back when* the norm was one or two sockets per room (at most), you would run your "ring" around the middle of the house taking the shortest route that visited each room. You'd have one socket in each room fed directly from the ring. Where you wanted a second socket, at the outer side of the house, you'd run a spur off the first socket in the room. Compared with an equivalent number of sockets, all on radial circuits, that was a significant saving in cable.
However, the real saving comes from having fused plugs - that's what makes the RFC practical. By having fused plugs, you could use fixed cabling and fusing that supported a "full load" (13A) at at least two sockets, while employing diversity to allow many more sockets. When it was introduced, the cable would be the old imperial size of 7/0.29 (said as "seven stroke oh two nine") which was roughly comparable to 2.5mm2 in metric cable. With a current carrying capacity of somewhere between "teens"A and 27A depending on whether fed by fuse or MCB (miniature circuit breaker), and how/where it's installed, as a radial it would not be allowed for it to be protected by a 30A fuse or 32A MCB. It's the division of current between the two routes (each way around the ring from the supply point) that makes it feasible - though there are issues if you have a lot of load close to the supply in one leg.
So the use of fused plugs allows the circuit to be fused at far greater than 13A (or the pre-BS1363 common size of 15A) and thus have "many" sockets on one circuit; and it's the ring arrangement that allows a smaller size cable to be used. Between them you save both on the length and copper content of cable needed.
These days, when there are less plug-in electric heaters used**, and a requirement for many more sockets feeding lower power equipment, there is a move back towards radial circuits. If you are a masochist, you can use 4mm2 cable and a 32A MCB. But more normally, you'd use a 20A MCB (or 25A if you can get them to fit the consumer unit) and 2.5mm2 cable. Particularly with the latter, you can do a new (re)wire with radials without significant penalty - as you point out, with the number of sockets needed these days, RFCs aren't the cable saving they once were. "Multiple" 20A or 25A radials also gives you better segregation if a circuit goes faulty - particularly now that RCBOs (residual current device with overcurrent protection - effectively and RCD (residual current device) and MCB in one device) are common and cheap, allowing a separate RCD per circuit.
* Don't forget that BS1363 which introduced us to our now ubiquitous square pin plugs with fuses was introduced in 1947.
** Given the standard arrangement of a single 15A socket in a couple of rooms, you could not plug in two powerful heaters into one socket without blowing the fuse. Having a 15A radial with more than one socket would be equally impractical. As an aside, at church we were without heating for a while due to a failed boiler, so we had to use fan heaters to take the chill off and keep our coats on. When a fuse blew, someone expressed surprise as he'd "used two different sockets" - without realising that they were on the same radial circuit and protected by a 15A rewirable fuse. I'd already worked out which sockets were on which circuit, and plugged one heater into each circuit - he'd moved one.
Going off on a tangent, BS1363 does not specify the dimensions for a socket. It specifies in detail the dimensions for the plugs (max/min pin size, pin spacing, even the shape of the ends of the pin. The requirements for the sockets are merely that they must accept any plug that is within the tolerances of the specification - e.g. maximum pin size without over-stretching any spring contact, and minimum pin size while still maintaining contact pressure. Do not ever plug in any of the so called "safety covers" as not one of them on the market complies with the dimensional standards of BS1363 and so can damage a socket - causing a fire later when there is nothing to connect the previous use of the safety cover with the failure. They also create a whole litany of other hazards that don't exist when they are not used. For more see the Fatally Flawed site.