Even a leisure battery.
I was just looking in the machine mart catalogue at a 750 watt inverter. That draws 62.5 amps at 12v. That's the equivilant of 14 car headlights all on at the same time. And most electric heaters draw either 1000w or 2000w depending on their design. That's like wanting to run the whole estate off your lounge wall socket. (hyperbole)
Spruce