From what you write, it sounds like your parents still see you as a child that doesn't know what it wants, instead of a 16-year-old who's almost reached the age of majority (or has reached it, depending on where in the UK you live...).
If this is true, then I doubt that there is much you can do in the short term to get them to listen to you. A few things might help in the long run, such as
- finding a good moment for conversations (e.g. when neither you nor
your parents are tired, angry or otherwise preoccupied or stressed)
- not getting too emotional when arguing with your parents
- giving them well-thought-out explanations for your views
- asking them to explain why they're holding their views, without letting yourself be talked into backing down on your own points. There might actually be good reasons why they think it's important for you to learn how to drive, and you should at least consider them, even if you won't let them change your mind.
- countering their arguments ("it will do you so much good to be able to drive") with alternatives ("I can take the bus to XY; there is a train running from A to B that only takes X minutes", "if I ever owned a car, the money I would have to pay for gas and insurance would amount to X pounds; with that money, I can instead .....")
- trying to find out why they think it's important to drive and adressing the fears that give rise to their views.
The last one seems important to me. I doubt that your parents treat you like a child on purpose. I think it's more likely that they're not used to you being able to look out for yourself. They might fear that they're not doing their job right if they don't prepare you for "real life", and that if you don't learn to drive now, you'll miss out and it will be their fault. Pressuring you into eating desert when you clearly didn't want any points into the same direction - "he'll miss out and be sorry afterwards". [I'm just assuming you're male - if you happen to be female, please excuse me]
I don't think this is something your parents consciously notice. So if you find out what their fears concerning you are (Do they think you won't find a good job if you can't drive? Are they scared you'll move away and not visit them? Are they afraid that if you can't drive, you'll walk home alone through a scary neighborhood? Do they think that the bigger your car, the more of a man you are?) and manage to allay them with well-reasoned arguments, that might go a long way towards making them listen to what you say.
In the short run, though, this is probably not going to help you. So:
Do you have another adult who does listen to you, and who your parents trust? Grandma, uncle, a teacher who likes you, anyone?
Can you get him/her to moderate a discussion between you and your parents? Don't let this person fight your fight for you - he/she's mostly there to make sure that your parents don't pressure you, and to support you when they're not listening to what you say.
If they pressure you into another driving lesson, talk to the driving instructor. Tell him you're scared of driving. Tell him you don't want the lessons. You might get lucky and get someone who understands that teaching someone who doesn't want to be taught and is actually afraid while being taught doesn't make sense, and he might suggest as much to your parents if you ask him to stop the lessons.
If that doesn't work, refuse to comply. In the worst case (e.g. if you actually find yourself sitting in the instructor's car), refuse to move the car. Nobody can make you do it; the driving instructor won't hit you, he won't scream at you, at most - if he's a bad teacher - he might try to make you ashamed, maybe by pointing out how that's never happened to him, or that you're wasting your parent's money or something like that. In fact, at your age, your parents probably can't actually force you to do anything you don't want to do, except by taking away privileges. If you refuse to comply, this will most likely escalate into an open conflict with your parents, so you should be ready for that. If they punish you for not complying, stay calm. Tell them you you're sorry for acting out, and you'll accept the punishment, and you know they only want what's best for you, but what's best for you is something you need to have a say in, and you won't change your mind on not wanting to drive. They can't ignore that forever.
Just like Becuzz, I don't like the "don't comply" suggestion, because it immediately paints you as immature when you do it (which is why you need to calmly accept any punishment and stay polite - to show your parents that you're not throwing a tantrum - you're defending your decision and accepting the consequences), because it escalates into a conflict and conflicts often yield unpredictable results, and because I'm a parent myself. However, at 16 you really should be given a say about decisions that concern you, and if they don't grant you that, refusal to cooperate is justified IMO.