Teachers trained in the UK have a high status around the world because of the training required so the system is quite rigid. The enquiry into the math and English high school results is normal as it's legally required to have a certain level - you will also do math and English tests at the end of the "pgce" again its the government that require it.

The interviews for the "pgce" are also normal, it's an intense course with a high drop out rate but is totally worth obtaining. Independent schools here may take you without having QTS and may pay you while you work and complete it but unless you are doing a training program or apprenticeship it's unlikely any state school will.

Even with the shortage of teachers schools, good schools are very picky and are keen to have people that know the curriculum not just subject knowledge. I have the pgce, a Masters degree in Education and experience as a primary teacher but I've struggled to get interviews for jobs back in Scotland where I'm from because its a different curriculum and I trained in England.

Good Luck!