The fire was in an office where there was one double socket that had, IIRC a PC,a printer, a kettle, a walkie talkie battery charger and a fan heater connected to it via multi plug adapters.
Unsurprisingly the wiring eventually gave up and burst into flames
As long as the kettle was in one socket and the rest connected to the other, that should be fine...
If all hanging off one socket, it might not be quite enough to blow a 13A fuse (20A?) but surely still shouldn't be a problem unless the wiring is faulty (poor contact, incorrect conductor size), the cable is damaged or similar.
I'd guess the most likely candidates are faults in the battery charger PSU or the heater, but the latter would probably be obvious.