Adding from the child's perspective! I'm now 22 but thought I would share what happened with me! For reference, friends with some people in comfortable situations, some "average" income friends (parents) and me having grown up in a less than fortunate position.
Lessons were DDad paid for 2 Step Mum at the time paid for 2, DM paid for 2 (plus provisional) and my Nana paid for 2. I ended up having weekly lessons for almost 2 years (some missed lessons due to working hours). Lessons were £26 an hour. I was an apprentice earning £3.30 an hour, then it raised to about £5.50 an hour when I finished the apprenticeship and went to college full time too. I paid the remaining lessons (although, for transparency, my driving instructor was amazing and gifted me 15 sessions over the time I was with her).
Tests, DM paid for the first one (I took over 10 due to anxiety and being stalked on tests which meant we had to stop for my safety and examiners safety) and my driving instructor paid for my final one. I am aware this is not the norm and I was very fortunate!
Cars - my DSis sold my mum her 97 Ford Fiesta for about £80, it sat in the garage for over a year (had no MOT) when I passed my test, it was scrapped as no chance of passing MOT without being very expensive and my Nana referred to it as a death trap. Made £20 profit on scrapping too!
My Nan then kindly offered to pay for my first car, on the agreement that I paid it back monthly. It was a Fiat 500 (from a garage but was 2012 model, not new £6000) and an amazing first car! Condition of buying from garage was set by Nana, she would not have loaned the money if the car was not from a garage. I then paid £180/£200 a month to her. When I got to the remaining £2000 - I was moving over 100 miles away so she kindly said the repayments were finished so I could focus on starting fresh in my new area.
Insurance- my insurance was £80 a month on Fiat 500 when I first passed, I paid this myself.
Sorry so long winded! Hope this might help with how things worked for me!