Then we need to start pulling it apart in other places
Your light switch shows 3 switches. If only one of them is being used for the problem lights and the other two serve lights that have not been disturbed, then leave them alone and don't consider them. Pull the switch off and label up the wire that goes to the particular switch that used to operate this light (you should be able to see which switch goes to which wire just by physical correlation) with an A, 1 or something. If there are multiple wires to the switch, use different letters
If there is another switch elsewhere that also controlled the problem lights, pull that switch off and find the relevant wire and label it again with totally different letters (once you work out which wires go to where you can either relabel them or write a map of a<->b etc)
Once you've got your switch wires labelled up, clip a 9V (or 1.5v, or whatever) battery onto one pair of wires from them (handy if you get some crocodile clips on a wire) and go round with your multimeter (buy a cheap one) finding the other end of the wire that shows 9V. Remember that most meters have a different switch setting for AC vs DC (DC is a solid line and dotted line, AC is a wiggly line). Remember that at least one wire in the ceiling you've shown us will go to the other light fitting (you said there were 2 luminaires, right?), one wire will come from the last light or fuse box, one wire goes to the next light. The 9v battery means you can detect voltages when the mains it turned off - turn the mains off when doing this. About the only time you might want to use 240v for diagnostic is when working out which wire comes from the fusebox, and you can't be bothered disconnecting the fuse box end in order to clip the 9v battery in) but remember that gripping a hold of a wire with 240v on could kill you, so do work safely.
You need to get to a situation where you know, for all those wires in the ceiling, where they go and how many cores in them. Once you have that you can draw us a sketch of what it looks like, all labelled up with your letters, and we can tell you "at the light, put the BLACKS from wires D F and G into one junction block, along with the neutral of the new light fitting you want to install.. put the reds from D A and F into a junction block, put the black from B into the live of the new light fitting.." and we can just do this as electrics by numbers
Handy for your 9v battery, should be a couple of quid:
£8 for a multimeter, will come in handy for all sorts even stuff like checking fuses are blown or AA batteries are dead:
https://www.screwfix.com/p/lap-ac-dc-digital-multimeter-600v/75337
Which mode to use depends on whether you're checking for 9v DC battery or 240v AC power. Use the range that is higher than your max (put it on 600v AC for testing UK power)
Do not use A (amps) testing mode; you'll blow the fuse in the meter for sure. Only use V (volts) testing mode