What is the black colour wire in a 4 wires cable? Live? Neutral?

That appears to be a four core flex for connecting some sort of an appliance, like a storage heater to its control gear, so the black wire is probably some sort of control wire.

What does the other end connect to, and why are you wiring it to a socket?

Can’t really tell but that doesn’t look like 2.5mm cable that you’d normally use in a ring main.

Is there another wire as normally you’d have 2? If not then that plug could be a sour in which case I’d try and find out where it’s spurred from and check how it’s wired at that plug ie is only brown used or are both black and brown used and connected to L.

Assume nothing, get a multimeter and test.

Just because brown is supposed to be live, there is no guarantee that an idiot DIYer or drunk sparkie didn't actually use it as an earth.

It's not possible to give a definitive answer from the photo. At a minimum you need to test the wires and/or trace the cable back to see how it's connected.

You could also consider:
- the size of the cable?
- which circuit is it on?
- the protection, eg. mcb, fuse, RCD?
- the original purpose of the cable?

The colours of the wires is unusual. Three core & earth is often coloured for three phases, so brown, black and grey. To have brown, black and blue suggests two phase and neutral which is unusual in this country. I wondered if it could be from a European hob. Perhaps the supply end comes from the cooker connection on the wall, fed from an isolator above the worktop. Maybe the OP has removed the load end from the hob and wants to install a socket in a cabinet instead. This may well be possible but you should be aware of what you are doing.