Yes, my Mum taught me in our family car. I passed first time.
I taught our son in our family car. He passed first time.
A lot of it is confidence (both you and your child). My father tried to take me out a couple of times but it was a disaster as he was a nervous wreck constantly telling me to slow down, watch the pedestrian, etc etc whereas I was pretty confident and competent, but he didn't know that. It was the same with our son, when OH took him out, son said the same, it really put him off that OH was always on at him to watch things he'd already seen etc. I do think it's better on a semi-permanent one to one basis rather than different people.
The key is to start somewhere safe and remote with minimal (preferably no) other traffic such as an industrial estate in the evening or Sunday, or a supermarket/retail car park when it's closed. Get them used to "driving" the car, i.e. braking, acceleration, gear changes, steering, starting/stopping without stalling, etc without the worry of other road users. That's actually the pretty easy bit as it's just lots of practice. You can practice parking at this level too!
Once they can technically "drive" the car to a safe level, i.e. able to jam on the brakes if told to do so, and drive at such a speed as to not annoy other motorists (i.e. not at a snail's pace as stalling everywhere), then it's time to drive around other vehicles, such as minor roads, housing estates, etc. so they can start to get used to driving with others around, looking for road signs, road markings, etc.
After that, it's main roads, roundabouts, traffic lights, dual carriageways, etc., just avoid rush hour and school start/finish times when there are loads of idiots around.
After that, everything goes, even rush hour, traffic queues/congestion, school run times, etc. and then it's time for the test.