I have a loft light which is wired into the hall light. I can turn on the loft light on its own( light is dull), but if I turn on both lights they go very dim. Looking at the wiring, there is three core wiring from hall connection to loft light switch but then there is only twin core to light bulb ( no earth). Would this lack of earth between light switch and socket be the problem ?

in a properly wired circuit, no.
Recall many years ago none of our wiring systems used earth or more accurately, grounding conductors and it worked fine. Grounding conductors and connections are used for personnel and equipment safety.
If you are looking to correct this issue you should hire a pro with a good voltage meter...

Sounds like they may be series wired rather than parallel.