Martin Angove wrote:
Was in a house the other day where as far as I could tell there were
four radial circuits feeding sockets, all fed from the same 20A fuse.

Which is perfectly normal and correct if I understand you correctly.
A 20 amp protected radial wired with 2.5sq mm supplying sockets can be
branched as much as you want. The branches can be at the consumer unit
as well as elsewhere in the circuit.

The main limiting factor on this type of circuit is that it should serve
a maximum floor area of 50 square metres. Also, of course, it should
be capable of supplying the devices connected to it (subject to
diversity).

--
Chris Green