I'm with natwest so I'm not sure about other banks. I could get an overdraft of up to £2000 during my final year of uni, during my first year post-graduation I kept this overdraft interest free, the next year it was £1000 interest free and in the third year my interest free overdraft went to £0, I could still have an overdraft but I have to pay fees (which are not much, makes less than £10 a month if I'm £1000 overdrawn)
so the bank will slowly reduce your overdraft with the expectation you pay it off until you start paying fees