That was my next step too, luckily all cables come from the top.Firstly, please tell us if the two lights are on the same circuit. That is - do they both stop working when one breaker is switched off (or one fuse is removed)?
IF that is the case, then remove the link wire and tell us if both lights still work.
Is there a loft above this, can you see where the cables go?
EDIT: I'm getting confused, Initially I thought these looked like 3/0.029 (but a closer look shows it's solid conductor) however the earth wire looks stranded, either that or it's more than one solid wire.
I think this looks like 2x T&E but it could be 4x 1c&E
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