What is the tool I need to cut around the coving to be able to drop down an old lathe and plaster ceiling?
I have heard about an adjustable depth small circular saw thing?

A 4" chasing tool (like an angle grinder with a dust shield and takeoff)?

AEG – Atlas Copco used to make one.

Am I after one of these?
wall chaser?

To drop the old lathe and plaster ceiling you just need a reasonable hand saw and some pateince.An angle grinder/ wall chaser will just burn the wooden lathes, make alot of dust and smoke and not work very well.The problems will come when the old ceiling is down and you try to put up the new plasterboard as there will be no joists/noggins at the edge of the existing cornice.

So how do I keep the 100+ year old intact ornate coving, but replace the artex coating lathe and plaster that has seen better days?

skim?

What TJ said.

Scrape off the biggest lumps of old artex, then score it with a Stanley-knife. Give it a coat of PVA to help the new plaster adhere to the old.

BTW some old artex contains asbestos so you might want to get it checked?

Guy is skimming next week.