What you seem to be talking about is a power inverter.
12VDc - 240V (Cigarette to 3-pin Mains).
I have a 150W one that i bought from maplin about 6months ago there good for running small devices, I use mine to power my laptop, Charge Cameras, 2-way Radios etc.
There good but you need to be carefull, they can drain you battery pretty quickly and leave you stuck in the middle of nowhere, trust me i know.
I have a 150w work lamp and decided to "try it out" on a camping weekend, it lasted <10min before cutting out and leaving my car battery dead. thankfully i got a jump and everything was OK again, The car battery is and was fine (had it checked) so i can only blame the inverter.
I only really use mine with the engine running now, charging my 2-way radios is ok thou they use a small amount of power so i can happily leave them for a couple of hours on charge or use my laptop parked at the beach for an hour or so (both with engine off)
I'd imagine a hoover would use a lot of power and may even require more than the inverter can give so be careful..
out of interest, mine was £14.99 from Maplin