As pointed out above – confidentiality can be implied but they should really have taken steps by getting you to sign a confidentiality agreement. The other thing a judge would look at if this came to court would be any precedence with other former employees – if they haven't enforced confidenitality in the past then they will be on very weak ground.
If they are sensible about it they should get you to sign a compromise agreement (which could include some clauses on confidentiality)offering you some form of moentary recompense. Just sign a confidentiality agreement without getting some form of legal advice first – tell your eomployer that and get them to pay for it.
Be careful if they make you work your notice that you don't take anything that could be deemed to be confidential. If they are worried about it get them to spell out what they deem as confidential but don't sign anything.