Newbie basic electrical wiring question

[Horndogg81]

Hi all,
My first post on DIYNot forums.
I'm looking to replace the outside flood light on my garage with a Ring flood light current/old light shown in pic). The light is hardwired and connects via this white junction box (second pic).

The brown cable from the white junction runs down between the facia and wall into the light.
Unfortunately the earth in the brown cable has been cut short and is to short to reach the earth connection on the Ring light so I need to replace it.
Is this brown cable just 3 core flex 1.5 - or how do I tell? Does it need to be externally rated?

3 Core 3183Y Black Round Flexible Cable - 1.5mm2 - 5m | Wickes.co.uk

3 Core 3183Y Black Round Flexible Cable - 1.5mm2 - 5m

www.wickes.co.uk

Although this flex cable from Wickes is not external rated, can it be used or would someone share what type of cable I should be using for this please?
It feels silly to call out an electrician for what seems to be a simple job, although I'm happy to if needed.

Thanks all

 

[CountryFan]

Have a look at the cable along it’s length where possible, there’s usually some writing on it, possibly the same colour as the cable.

 

[TonyW2]

Can't see too welĺ, but can you confirm that the grey cables are separate from the junction box & it has only brown and white cables involved with the light fitting?
If so, is there not enough spare in the white cable to move the box
towards the brown cable then shorten it?
However the box needs to be fixed securely in any case.
Is it sitting on the wood in an external place?
If the brown wire has to be replaced, would it be easy to follow the white cable back and replace the entire supply w with one decent well clipped length of external cable.?

 

[securespark]

That white box looks like a flex connector and the brown flex looks like the sort of brassy coloured flex used for table lamps.

I might be wrong. But if it is, the flex connector may only have two terminals, hence why the CPC (earth) is cut off.

Am I correct in thinking the white flex goes to the supply and the brassy one to the outside light?

Is the supply cable plugged in somewhere?