Well, without knowing which airline in particular it'll be a bit hard to answer. However, they are probably asking that you hold either a JAR licence OR a CAA licence.
People who got their licences before the JAR system started will have the old CAA issued licence. As this was valid for life, there is no need for these people to convert over to a JAR licence.
If you have a JAR licence issued by the CAA then this is good enough.