If it needs to go off, then it does.
Most larger areas have link boxes on the LV to allow some loads to be supported by other substations. Bear in mind that in a city or industrial/business area the HV is almost certainly in a ring so the affected section should be able to be switched out with no loss of supply.
When the UK built it's networks, someone thought about maintaining them so it's always been designed that way.
I sit a bit on both sides of the meter as a lot of my companies business is on the consumer's side including overhead lines and underground distribution but equally I spend a lot of my time with the guys from the local network operator and various contractors sorting installs of new substations and HV network.
Stu