Yes, you should be able to open a bank account. Your credit rating still won't be very good but it shouldn't stop you opening an account. Some banks ask for a copy of the discharge certificate. You can get this from the court where you were declared BR but it costs £60.
The other option is to print off a copy of the Insolvency Register that shows you are discharged but this only appears for 3 months following your discharge and then you are removed from the Register.
If you didn't manage to print off a copy of the Register showing you are discharged then you should try to open an account and see what the bank says. You don't need to advise them that you were BR unless they ask. Some banks may refuse you point blank but others may be ok. You can open most accounts online now so there is no need to go to a branch.
If you find that banks need the discharge certificate then you will need to contact the court where you were BR and pay the £60 fee.