There are no correct way to go about an initial job interview; there are so many different environments and interviewers so no one rule applied to all. There are some unwritten rules though, and you should ideally stick to them if you want to proceed and gain the job or a second interview for your desired teaching position.
The main unwritten rule is to never be late. Blaming the traffic or the London strike is just not good enough, and if you’re late on your interview the employer is likely to imagine that you’ll be late throughout your time in their company.
The second unwritten rule is to show interest. No matter what job you’re going for you have to show some interest, otherwise they’re not going to take you on. If you dress to impress, listen when you need to and raise questions then you can show you’re keen and it’s important if you want to beat your competition.