Not at all.
I'm a primary teacher and we have a colleague who decided to become a teacher after working as an LSA in school for years. She's 43 and is now halfway through her 2 year training course (she is doing on-the-job training, so is doing a class share, working alongside another teacher as an unqualified teacher, gradually increasing the amount that she teaches and taking more control of the class. She gets paid a fairly decent amount too, given that she is unqualified. Obviously you don't get this as a 'normal' student).
It's a tough, but very rewarding career, and I absolutely love my job, and think I'm good at it, even though Mr Gove keeps telling us all how much we're failing our pupils
.
Like others have said, you need A-Levels. If you want to do a degree in a specific area first, then you can do a PGCE afterwards.
A primary teaching degree is a 4 year course at some unis, a 3 year at others.
I would personally say that I think a PGCE is more suited to those wanting to be secondary teachers, who want to teach the subject they have done their degree in. I did the 4 year Primary Ed course and I don't think I would have felt prepared to teach 12 subjects, as well as learning classroom management skills, etc, after doing a 1-year PGCE. PGCEs are extremely intensive.