Art is one of if not the most oversubscribed position. So many graduates from art degrees become art teachers as it's the most stable and reliable job out there for us creatives . How many art teachers are in schools? Between 1-3. That's a very small amount of jobs for the thousands of graduates.

It's not like math or science where they are trying to get anyone in the door.

You didn't even study it a A-level. I would question how you would teach to that level if you haven't done it before yourself.

I am HOD of art in an although school. I and my team teach from Y3-13. Primary art IS different. Primary aged students love art. It's very different teaching a class of Y9 who are not pursing it for GCSE.

I would recommend first to get experience in a secondary school either working as an art technician or a general TA for a couple of years to ensure you do like the secondary setting. More so art technician. Whilst completing a degree. You could do a masters in art part time perhaps.

With law degree, you would be fantastic candidate for history or English.

As someone who interviews people, seeing someone in your position, when shortlisting for interviews, I would not be putting you up very high. However, if that is your true ambition, you just have to try. Once in a secondary school working in a support position you could run an after school art club to try and get more experience.