Open 2 or 3, some will want you to deposit so much money before they will give you first £1000 of the overdraft, Abbey do i know that.
One you have the full overdraft with one, open another and transfer most of it to the new account so they will give you the full allowance with that one.
When you have all 3 maxed out, say you opened abbey, Lloyds and Halifax this would get you about £3500 of interest free overdraft in the first year, open savings accounts and put most of it in that to make you free money.
Then make sure you deposit "some" money into each every month, Natwest for instance get shirty if you don’t deposit £25 each month.
I then opened a cash back credit card with a high street bank with the usual 56 day grace period to pay it off, use that for all your spending which then gives you time to funnel the money around your accounts using online banking to pay it off (this also earns you free money through the cash back), and you have better protection against fraud.
If you can’t find a suitable cash back credit card then there is the abbey/Santander zero credit card if you go abroad at all as its free to use abroad, and maybe also consider the Lloyds Air miles duo card for the Air miles as you get quite a few for free at the moment for opening an account.
Obviously the usual rules apply with a credit card in that you need to respect it and not spend what you can’t afford to pay off.
Also to try to get the limit raised every time you talk to them as after a while you may get offers through allowing you to buy things interest free for x months which you can exploit more if you have a higher limit
Don’t forget every year they will allow you to increase the overdraft as the guy above says, and at the end of the degree you can make it into a graduate account with an even higher overdraft which will make you more free money.