Nomenclature is (or should be) significant!
The initial photo shows three
cables, labeled "1", "2" and "3".
doog442 asserts that "I've identified the neutral on the cable on the left (1) as being the switched live"
(which should have been written as "Switched
Line")
Hence, one or other of cables "2" and "3" must come from the Supply and the (remaining) "other" goes to one or more other "Light Fittings".
EFLImpudence then wrote
No, you have identified the black wire on the left as the switch cable.
However, a "wire" is not (necessarily) a "cable" - unless it is a single wire (double insulated)
within a "cable"!
(The [Twin and Earth] cable [1] on the Left is [presumably] a "Switched Loop"
cable.)
A "convention" is that, in a "Switched Loop", the Black (insulated)
wire should be the "Line" conductor, with the "
Switched Line" conductor being the Red (insulated) - returning - conductor
and
that the Black (insulated) conductor
should be
re-designated with "Tape", "Shrink Tubing" or other such "Permanent Marking".
If
doog442 is correct,
the Red insulated conductors of cables "2" and "3" should be joined together - together with the
re-designated Black (insulated) wire of cable "1".
The Black insulated conductors of cables 2" and "3" should be joined together and connected to the "Neutral" connection of the new Light Fitting.
The Red insulated conductor of the "Switched Loop"
cable "1" should connect to the "Line" of the new "Light Fitting".
(All "Earth" conductors should be "joined", including any/that of the Light Fitting..)