The HC1 form is only to determine if you're eligible for reduced costs or free dental treatment on the NHS.
You can already get NHS treatment without it, but you will have to pay something (it is nowhere near the costs of private treatment though). How much you pay depends on what treatment you need but the most you will ever pay for a course of treatment-which will be everything you need no matter how many appointments you have-will be about £200 in England (or £177 in Wales). If your jaw problem means you need orthodontic work, this will most likely be what you'll pay.
You might as well apply for the HC1 form and see if you are entitled to any reduction of the costs, but if you don't, you can always get an initial consultation and see what they reckon you'd need doing before deciding whether it's worth the cost (which will only be £17.50).
I've had a load of dental treatment recently (three appointments, two an hour long, an extraction, a root canal sorted out and a custom filling made for it, and have one more left to have all my normal fillings done) and personally I think it's a bargain for £177 (live in Wales).