If you read my post, you'll see I said qualified, as in having QTS.
It's true that in an academy or free school, you can teach as an unqualified teacher, but I'm not sure why anyone would want to. As you say, they're cheap for the school- starting salary is just over £19,000 and the maximum you can earn after 6 rounds of pay progression (not guaranteed to happen yearly) is just over £30,000. An ECT will be earning a comparable wage in their second year of teaching (just about £300 less), by their third year of teaching, they will be earning more.
The career progression for unqualified teachers is generally rubbish- I've never known an employer allow them to hold a TLR, or progress into any form of middle leadership. You're also potentially only employable in that school, or that MAT, so if they choose to mess you around, or reduce your hours, or similar, you're stuck.
I've also seen a situation where a MAT took over a struggling school and replaced all the unqualified teachers with qualified ones (the number of unqualified teachers was mentioned on their OFSTED, I believe) and the unqualified teachers were made redundant- this couldn't happen to qualified classroom teachers in the same way.
So, yes, it's possible to teach a class without having any qualifications, but I'm really not sure why anyone would put themselves in the position of doing a job for poor pay and less good working conditions, when you could suck up 3 years at uni, and go into the profession on a higher salary than you'd be on after 3 years as an unqualfied teacher?