So, I have an EV (Leaf) which would benefit from the ability to charge
using more than a 13Amp socket can supply. The supplied charging
unit/cable limits to about 10A, but the car's on board charger can
accept up to 3.3kW (some say 3.6kW).
This would need a different EVSE than the supplied unit, AND a beefier
mains socket.

Is it OK, in terms of building regs etc, to have a Schuko 16A socket on
a radial from the CU?

I know I can get a proper home charge point installed, but that's not
the cheapest option.
TIA.