As a graduate there is an option that you may consider for your route into teaching, by training in a school environment. School Centred Initial Teacher Training (SCITT) lets you get out of the lecture theatres, and allows you to learn directly from experienced teachers in a school environment.
SCITT leads towards Qualified Teacher Status (QTS), and many courses will also award you the postgraduate certificate in education (PGCE).
To qualify for a SCITT course you need a UK degree or equivalent qualification in a relevant subject to the one you wish to teach. (Primary teachers should relate to the national curriculum's core subjects). You may be able to take a pre-training course in the relevant subject if your degree is not suitable.
You will also need to have achieved a C grade in GCSE English language and mathematics (or equivalent).
How to Apply
You will need to apply for SCITT through the graduate teacher-training registry (GTTR), though a few providers will require direct applications.
You are allowed to apply for up to four providers, in order of your preference.
You should apply for the SCIIT course the year before you intend to study as the courses have to follow the academic calendar, so your training will start around September/October.