My mum is a driving instructor so I can give you some insight into how she did it and how she finds it! You do have to be committed to the training as it's not easy and if I remember rightly costs a couple of thousand to do and you need to have time, particularly for part 3 where you start learning how to instruct. My mum is with LDC and has been an instructor for maybe 4 or 5 years now. I'm not sure why she chose LDC, I think it may have been because they didn't have many instructors in our area so she figured that any potential students they had from our area would be sent her way, making getting work a little bit easier!
From what I know I think it's best to start off with a franchise unless you're prepared to really go round and drum up your own business. As you get more well known you will probably get most of your referrals by word of mouth but to start it can be quite difficult to get pupils.
How much you earn depends entirely on how much you charge and how many hours you're willing to work. You also need to take into account the cost of paying for the franchise, petrol, the vehicle etc etc. Some driving schools (which I won't name!) have such high franchise fees that their driving instructors have to work a stupid amount of hours a week to cover them and try and earn a decent living. You also have to be very flexible with your working hours because you have to work when your pupils want to have lessons and if you're too fussy about your working hours then you'll find it hard to get business unless you're the sort of instructor who has a waiting list and can pick and choose their own hours! My mum tends to work 6/7 days a week, most of the time she has her evenings free but sometimes she has to work them, and usually she will work all weekend. Her free time is generally in the evenings and she might have a spare hour here and there throughout the day. You have to take into account the time spent driving between lessons can take a big chunk out of your day as well so it's all about being very well organised! I would imagine that most places saying you can earn over £30k a year are expecting you to work a lot of hours every week. You also have to take into account that at certain times of year business can drop, for my mum I know that approaching December (Christmas) and at the start of the year, times when people generally have less money or are saving it for something else, people will have less lessons, but in summer she gets a lot of university and college students wanting to take lots of lessons in the hope that they can pass before September when they go back.
Overall, I think that at first a franchise is the way to go, though I know that my mum sometimes finds that her franchise give her details to pupils who are not in her area or more 'difficult' pupils. You have to be very well organised and very flexible in order to earn a good wage and you need to be able to market yourself. My mum often finds that if she gets the first of a group of friends to turn 17, they will recommend her to their friends and as they each turn 17 they will start driving lessons with her too. I've also made her a website and she's on a lot of directories, very high on google etc! You need to consider running/franchise costs and that your income isn't guaranteed and that it is hard work, just like any job! You might also want to consider how many other instructors there are in your area, who their franchise is etc to see how competitive it's going to be to get pupils. In this respect the more services you can offer the better (pass plus and things), competitive pricing and I've even seen some driving schools offering presents and prizes when you pass with them! Finally, be prepared to have last minute cancellations, changes, people calling trying to book a lesson for that afternoon and making things a bit more difficult!