You are quite right Western Power got swallowed up by the national grid a couple of years ago.
DNO’s work in strange ways – they may send someone out check, who may upgrade the cut-out, or they could send another bod out another day! Either way you your first visit should be within 10 days, as said previous.
National grid, will only upgrade the cut-out fuse to a maximum of 80A in 99&% of cases, which they aren’t the only ones starting to do this (Northern Power is another)
A CT clamp will be installed with the charger, this will monitor and reduce load to the charger if necessary. Due Diversity being a factor with electrical installations, the chances of everthing in the house being on at the same, whils’t charging, would be highly unlikely night or day, the charger will perform as required anyway.
If your existing cut-out is 100A, it will be left.
Whether or not they will upgrade you to split or three phase, is up to them on the day. It’s unlikely.