Yours seems to be a fairly bog-ordinary ceramic halogen hob.
There's unlikely to be a fuse inside.
My guess would be the supply to the hob has failed at some point
You say the hob is hardwired separate from the oven which is still working.
I assume you mean hardwired as distinct from being plugged in. If it is plugged, it may be worth checking the fuse in the plug.
What sort of hardwiring point is the hob connected to? Some have an integral fuseholder you can access from the front. Here's a bunch of typical items:
https://www.google.co.uk/search?q=fused+outlet&safe=off&sa=X&tbm=isch&tbo=u&source=univ&ved=0ahUKEwiSk_SFsczVAhWEExoKHeyFArUQsAQISw&biw=1861&bih=1028
Have you checked in the fusebox (AKA: Consumer Unit) for any breakers that may have tripped? If the breakers are not properly labeled now might be a good time to sort out some proper, neat, legible labelling :-).
If there's a breaker which is tripped, make sure everything on the hob is off and switch it back on.
Turn the items on the hob on, one at a time. If it trips out again, there is a problem with the hob or wiring.
If it gets more complicated that that - or if you are in any way unsure - consider asking a competent person to look at it
Acp, August 2017