As somebody who has owned a car and not owned a car for various reason at various times, it's considerably cheaper without one. My travel costs are around £500-£1000 per year, compared to £5-6,000 per year with one. £5000k I can spend on other things.
The average cost for running a car in the UK is £6k per year, and 50p a mile if you are doing 12,000 miles, rising to 77p a mile if you are doing 8,000.
Yes you can get bangers, but I prefer something more reliable.
Like-for-like public transport can be cheaper (as low as 10p a mile or less for rovers and advance tickets) but it depends on the times, tickets, how many people are in the car, whether you are travelling on rovers, group save or rail cards, on or off peak and the type of car.
Most journeys in the UK are less than 5 miles, doing school runs, to the shops and so on. When you don't have a car, you tend to walk (possibly cycle more) for these journeys, which is free, or virtually free. The added bonus is of course health benefits. The internet really helps these days for shopping, so there's not all that many times, unless you live out in the middle of nowhere or reach those sorts of places you miss having a car.
Ideally, in real life, if you can afford a car or can drive, I'd argue for a careful balance for walking, using public transport and possibly cycling, as well as using the car. That way you get all the convenience (driving in cities isn't that convenient, but out in the middle of the sticks it is), health benefits, reduce congestion, and you save some money.