How To Spend Time

I can only answer this question about how to become a secondary school teacher in science or math from my perspective in the U.S. It may be helpful but it won’t fully apply in the UK.
The first thing an aspiring teacher of math or science does is to have a Bachelor’s degree with a major in one of those two areas. However, even if the major area was not in math or science. one could take perhaps four to five courses in one of those areas above the bachelor’s degree to be academically qualified to teach either of those subjects at the secondary level. Given that was done, then an application for a teaching certificate for teaching at the secondary level should go to the Education Department of the state where this candidate resides. After about six weeks and a fee payment, the appropriate teaching certificate would be granted to the candidate, and the candidate would look for a job teaching in that field.
Not withstanding, that person may and could be teaching in that field without a teaching certificate because the school district or the Department of Education in that state can grant a temporary certificate or a provisional certificate that allows the person to continue in his or her position for a limited period of time that sometime could be extended for years.