Is it possible to run a 13 amp plug from a car if you have the right adaptor?

Household vacuum cleaners can draw over 10 ampere off house mains ( 2500+ watt in some cases ) so you are going to need one large inverter. Too big to draw power through the cigar lighter. Have a look around to see if you can hire a petrol powered generator for a few hours to do the job. ( HSS for example ) A lot cheaper