You can contact a journalist at the BBC through email or telephone. You may get the contact address of the journalists at BBC through the official website of BBC. It might consist of information about their journalists and the places where they can be contacted personally. You can also try calling up the board line number at the BBC and asking them to put you in contact with the required journalist or give you a number where the journalist can be reached or provide you with the email id of the journalist.
As journalists are on look out for news and stories you may get to talk to them if you have a story that might interest them. There is also an underground network of journalists which contain sources who give tip offs and hints about various happenings and if you manage to get in touch with one of the sources then even they can give you the email id or any other means of contacting a journalist at the BBC. But the last method is highly improbable because the identities of sources are very closely guarded.
As journalists are on look out for news and stories you may get to talk to them if you have a story that might interest them. There is also an underground network of journalists which contain sources who give tip offs and hints about various happenings and if you manage to get in touch with one of the sources then even they can give you the email id or any other means of contacting a journalist at the BBC. But the last method is highly improbable because the identities of sources are very closely guarded.