TheScullster wrote:

Currently the sockets in the extension are a radial spur from the breaker
covering the upstairs main house ring main

A spur from the origin is perfectly valid, but to count as a
'conventional circuit' it should obey the usual spur rules, i.e. feed no
more than one single or double socket or else be fused down to 13 A.
Also the whole area served should remain within 100 m^2. You mention
three single sockets on this spur - are they wired in 2.5 mm^2 cable or
4 mm^2? The circuit would not comply with BS 7671 (== IEE regs. 16th
ed. as amended) if the former (unless it is a fused spur) but may comply
in the latter case as a special design. On the whole though it sounds
like a cowboy job as the rules hare haven't really changed since the
'60s (if not before).

Similarly the extension lighting is a radial spur from the upstairs lighting
feed

No problem there, necessarily, provided that the total load (assume 100
W per lampholder) stays within the cable and breaker ratings.
Nevertheless it is considered desirable to spread lighting over a
reasonable no. of separate circuits to avoid the problems of sudden
total darkness in the event of a fault or nuisance trip.

Is it a big no-no to power more than one circuit from a single breaker?

Whatever you feed from one breaker is /ipso facto/ a single final
circuit. What you have is composite circuits with multiple parts or
sections.

There are currently 3 single sockets in the extension, so I presume that the
power to this room should be converted into a ring whether it returns to a
shared fuse or not?

What floor area? A (separate) 20 A radial circuit would be OK for
general use if it's under 50 m^2. (Assuming no major kitchen/laundry
appliances or water heaters are involved.)

There are currently no spare fuse ways in the CU so it would be an expensive
upgrade for one room to provide individual protection for these two
supplies.

From the date I'm imagining a Wylex-type brown consumer unit with
rewireable fuses, or perhaps BS 1361 cartridge fuses. Nothing wrong
with those /per se/ until you start to run out of fuseways.

Perhaps it's time to bite the bullet and invest in an upgrade to a
modern split-load MCB consumer unit. Sort out the extension power
circuit and provide a few spare ways, and RCD protection for the socket
circuits too.

HTH
--
Andy