I studied at a non-UK university

Overseas qualified teachers
If you have qualified as a teacher inside the European Union, you should be able to access teaching positions as if you trained in the UK.

If you qualified outside the European Economic Area, you will need to gain Qualified Teacher Status to teach long-term in the UK. The National College for Teaching and Leadership runs an Overseas Trained Teacher Programme which will get you to this stage.

Graduates from overseas universities wishing to train to teach in the UK
The first thing you need to do is to have your degree evaluated so that it can be compared to an equivalent UK qualification. 

Get in touch with the National Academic Recognition Information Centre (NARIC) who will give you a letter of comparability. 

You will then be in a position to approach teacher training providers to find out if your qualifications make you eligible to apply for their courses.