Lord Irvine argues that there would be a desire among judges to use their new powers under the convention - which enshrines the right to personal privacy - to create new law on a case-by-case basis. That might lead to pressure for the Government to step in with its own legislation, he says in an interview with today's Observer.
However, the Lord Chancellor made clear that the Government had no intention of legislating at present to bring in curbs on the press.
The issue caused deep friction between the government and the press during John Major's period in Downing Street. The last government threatened new laws, but ultimately failed to introduce any measures.
The Labour government, backed at the election by press allies very hostile to new curbs, is nevertheless committed to incorporating the convention.
In his interview Lord Irvine said that he detected a judicial appetite to develop a privacy law, which could be produced by test cases. "If you ask me 'what happens when you incorporate the European Convention on Human Rights and do you predict the courts will develop a law of privacy?', I say 'yes'."
However, some sources within the newspaper industry dispute the inevitability of the process Lord Irvine describes.
One said last night: "The industry believes there are methods of incorporation which would not allow a common law of privacy to be created by the back door, and these need to be fully explored."
This refers to an interpretation of the New Zealand model, based on the country's Bill of Rights, under which judges are prevented from ruling on matters not covered by statute.
Some argue that the European convention's reference to privacy is intended to protect individuals from intrusions by the state, rather than the press.