Reading The Electrician's Guide to the 17th Edition, first edition, by John Whitfield it says (pg 133) when talking about socket outlet circuits:

Generally, 0.5 mm² cords should be the smallest size connected to plugs fed by 30 A or 32 A ring circuits.

Apart from the following sentence, which discusses cords longer than 10 metres, it doesn't say anything more about minimum cord CSA for ring final circuits. Page 136, talking about radial circuits, says:

The minimum cross-sectional area for flexible cords should be:

0.5 mm² where the radial circuit is protected by a 16 A fuse or circuit breaker,
0.75 mm² for a 20 A fuse or circuit breaker,
or 1.0 mm² for a 30 A or 32 A fuse or circuit breaker.

Obvious question, why is is acceptable to plug a 0.5 mm² cord into a 32 A ring final circuit but not into a 20 A radial circuit?

Don't think so. All that says (immediately after the first sentence I quoted above) is:

Where the cord length must be 10 m or greater, the minimum size should be 0.75 mm² and rubber-insulated cords are preferred to those that are PVC insulated.

It's not completely clear if that applies just to ring final circuits or all socket circuits - it's in the more general section but immediately follows and qualifies a sentence which is specific to rings rather than radials.

Whatever, it still leaves the question of why it might be acceptable to plug a 0.75 mm² cord into a 32 A ring but not a 32 A radial.

(My interest in all this is that I plan not to bother with any rings in my house - mainly because I won't have the inverter power available to generate enough current to need them. Most sockets will be on low power radials off a small always-on inverter with a few socket pairs, mostly in the kitchen plus a few others, on their own individual cables off the higher-power inverter which is only run up when it's needed.)

Posted By: markocosicShort 0.5mm^2 cords can draw enough current in a fault condition to trip the breaker quickly before things get too hot. Long 0.5mm^2 cords are too high impedance to trip the breaker quickly enough to meet the regs.

Ah, that makes sense: it'd be an awfully long cord to stop 32 A flowing but it's easy to believe that the cable or whatever's actually shorting might catch fire before the breaker tripped at 50 amps or so. At 32 amps the temperature of the cable would initially rise by about 0.7 20 °C per second (¹)until heat loss cut it back but not by enough, I suspect.

Ring mains are an awful idea …

Indeed, a desperate war-time fail-dangerous invention we should have got rid of long ago.

We should be designing for 16A socket circuits as many continental market/chinese market devices commonly sold in shops do not have large enough conductors to trip the 32A breakers used in (UK only) ring circuits.

Yep - who needs or wants more than 6 kW on sockets? I'm planning 6, 10 or 16 amp MCBs on my low power radials and 16 or 20 A on the few high power socket pairs.

(¹) Oops, forgot the squared bit of I²R.

Who needs fuses? Over here (Italy) all plugs are without fuses, even on a 20A circuit, and safety is taken care of via an RCD and MCB. Of course you 'can' fit fuses to the socket but they take up a Gang and cost a lot.... and if you want a switch on your socket...yup each switch takes a gang and costs a lot, especially if you splash out on a double pole switch. So to achieve a UK std double socket you need to fill a 6 gang box and it will cost you over 40 Euros. What is needed is the best of both worlds.