I must admit I have never come across an old double fused service head where they could fit a solid link in the neutral as they were all rewireable fuse carriersMentioning a "burning smell" or similar usually motivates them.
It's possible that the neutral fuse has been replaced with a solid link?
How good is your hearing, can you not hear that faint crackling noise from the service head and report it.I've contacted UKPN emergencies department and they've also said I need to contact the supplier regarding the fused neutral. They require a B11 flow from the supplier.
But, for the black earth wire, they will be sending someone out to have a look soon.
I contacted E-On and the earliest appointment they've given me is 10th December - this is to attempt to install a smart meter which I assume they cannot and result in them reporting the situation to UKPN.
I have never known a DNO be so obstructive or ask me to contact the supplier when it comes to safety issues unless they react differently if it is an electrician calling them, in my local area both of the DNO's would be out within a few hours of being called with an issue like this and depending on how urgent it was considered the DNO guy would have a jointing team onsite within 2 - 3 hours if it was considered urgent or 24 - 48 hours for a less urgent job