BS1361 service head fuse blown

Need some advise as this is new territory to me.
Working in an engineering firm today and at 5pm the laser cutter stops and so do a few other bits of kit. Traced to loss of a phase due to the main service head fuse blown, each phase is fused at 100 amp. Owner call DNO who will send someone tomorrow. It transpires that this happened 2 months ago, same fuse. Tails extremely warm and fuseholder too hot to hold. Removed a fuse from the other end of the factory so they could finish of the job being cut. Amp clamped all phases.
Compressor and lots of small bits of kit 36 amps per phase, turn on the laser cutter whish start a filter system first and 60 amps per phase. Laser cutter kicks in and 97 amps per phase. This has been working hard all day from 7.30 am. Can not find any info in the red book on how long a 1361 at say 100 amps will operate for.
My question now being what is the max the DNO will upgrade the incoming fuses to? I have no idea what size the incoming cable is.
Any help from more experienced industrial sparks would be greatfully received.

If the fuse is rated 100A then it should operate indefinitely at that current...

Could be poor contact between fuse and holder. Were the tails warm all the way along or just towards the service head ?

Is there any new kit there or is it all existing ?

Could be a case where some inductive loads and the laser cutter have suddenly kicked in together and the fuse could not take the inrush perhaps.

Are the majority of the loads 3 phase or could some balancing up take place ?

Thanks for the replies,
The tail that ruptured the fuse was warm throughout its length of 8", the others were warm but not as. The fuseholder was so hot I dropped it when I pulled it out. When they had finished for the night I removed the replaced fuse and put it back into the other part of the factory, this was getting warm in only 20 minutes. I will get the DNO to check all connections tomorrow and also the replace the fuseholder.
The board is pretty well balances with all 3 phase equipment on and single phase sockets and lighting shared across all phases quite well. Poor connections may be the way to go as you could smell a bit of burning when you removed the fuse.
Thanks again.

In this case, luckily the fuse operated in order to cut off the supply (as it was meant to do!), I have heard of fires starting due to poor connections, so it is probably means that the DNO will need to replace an offending component or two.
On one job once, there was a faulty connection in a CU busbar, and the breaker on that connecton kept tripping out, due to the heat of the faulty joint - replaced the breaker involved and checked connections - fault solved.

Thanks Kai, I will check all the connections for the dissy board tomorrow.