It sounds to me like this policy was mis-sold. Why would a student with no job need a Personal Accident policy? The main purpose of such a policy is to replace your income should you become injured and need to take time off work. Of course, a lot of people's employers provide sick pay anyway, but this policy would be useful for those who aren't covered by a corporate sick pay scheme.
I would never buy a policy from a cold-caller. If I ever wanted to do so, I would ask them to send all the documentation before agreeing to anything. Personally I believe cold-calling is an appalling sales technique, as it doesn't give the customer time to think things over, and vulnerable people might feel pressurised into agreeing with the salesperson.
I have an account with the Halifax too, but luckily I've never had anyone try to sell me insurance. If they ever did, I would tell them that as I work in insurance anyway, I would be able to arrange a policy myself if I believed I required one!! That would soon scare them away from trying to mis-sell me a policy!!
What you need to do is write a formal letter of complaint saying that you were sold a policy you do not need, and ask for a full refund of any premiums you have already paid.