The most controversial aspects of the Leveson report into press regulation will be subject to a further consultation that will run into the new year, the Culture Secretary has announced.

The consultation will look into a provision in Lord Leveson’s recommendations that would compel publishers who don’t sign up to the new independent regulator to pay the legal costs of those who take action against them, even if their claims are unsuccessful.

It will also investigate whether it is in the public interest for the second part of the Leveson Inquiry, which deals specifically with phone hacking, to go ahead, given the costs involved and the failure of Operation Elveden - the investigation into the payment of public officials by journalists - to secure a single conviction.

She said: "Given the extent of these criminal investigations, the implementation of the recommendations from part one of the Leveson Inquiry and the cost to the taxpayer of the investigations in part one, which is £43.7 million and £5.4 million respectively, the Government is considering whether undertaking part two is still in the public interest.

"We are keen to take stock and seek the views of the public and interested parties, not least those who have been victims of press abuse.

"We will also formally consult Sir Brian Leveson on the question of part two at the appropriate time in his role as inquiry chair.

"I can announce that today we are launching a public consultation inviting comments on both Section 40 and part two of the Leveson Inquiry from organisations that are affected by it and from the public."

The announcement was heavily criticised by Labour’s Deputy Leader and prominent phone-hacking campaigner Tom Watson. He told the Commons: "We believe they have been discussed and debated enough, they should have been implemented years ago. The victims of press intrusion cannot wait a day longer."

He said the events of the past five years, including the jailing of "fake sheikh" Mazher Mahmood for tampering with evidence in the collapsed drugs trial of pop star Tulisa Contostavlos, made Leveson 2 "more urgent not less".