Culture Secretary Karen Bradley has denied kicking the Leveson Inquiry into the long grass as her predecessor cautioned against imposing huge costs on newspapers.

Ms Bradley told the Commons she is taking her time to listen to all sides before deciding what to do regarding the inquiry into press ethics and phone-hacking.

READ MORE: Labour calls for part two of Leveson inquiry

Labour MPs fear the Government is not committed to allowing the second part of the inquiry nor forcing newspapers to pay court costs in libel and privacy cases, whether they win or lose, if they are not part of a Leveson-compliant regulator.

Section 40 of the Crime and Courts Act 2013 has yet to be implemented, much to the frustration of victims of press abuse.

John Whittingdale, Conservative former culture secretary, warned imposing the cost penalties recommended by Leveson now would result in further losses of jobs and titles in the newspaper industry, something Ms Bradley recognised as a "dilemma".

Allegations of phone-hacking at the News of the World led to the Leveson Inquiry, with then prime minister David Cameron initially announcing in 2011 that it would be conducted in two parts.

The first reported in 2012 and examined the culture, practice and ethics of the press.

The second is expected to investigate law-breaking and improper conduct within media organisations, the original police investigation into phone-hacking and whether police were complicit in misconduct.

Labour's Graham Jones (Hyndburn) told Ms Bradley: "There's been some suggestion in the national press that this has been kicked into the long grass by ministers.

"What assurances can you give to the victims that this isn't being kicked into the long grass, Leveson part two will be implemented and we will see an end point to this?"

Ms Bradley replied: "You will know there are some pending cases and until those cases have been completed there can be no progress on Leveson two.

"But I can assure you that this is not being kicked into the long grass but we are looking very, very carefully at all the arguments on all sides to make sure we have that free press that protects the citizen."

Earlier, Mr Whittingdale asked if Ms Bradley shared his concerns about the continuing loss of national, regional and local newspaper jobs and titles.

READ MORE: Labour calls for part two of Leveson inquiry

He added: "Do you agree that there may be a case if there is a recognised regulator but its members are given the protection afforded under the Leveson recommendations, but would you also agree that to impose the cost penalties at this time simply would result in the loss of yet more newspapers?"

Ms Bradley replied: "You ... really do sum up the dilemma that we have. We do want to have a free press and we do want to make sure we have a strong and vibrant local press.

"I know from my local titles just how important that is to people."

She added: "They want to have that strong local press."

Labour former minister Chris Bryant welcomed Ms Bradley and her team of ministers, adding he is pleased Sports Minister Tracey Crouch is continuing in her post. He said he "daily wants to hug" her.

Mr Bryant went on: "As one of those who had their phones hacked in 2003, I just say to (Ms Bradley) that the victims of phone-hacking, many of whom were not politicians at all but victims of crime themselves... are desperate for the Government to stand by the promises it made to them.

"First of all that there would be Leveson two. Can you say that today? There's no reason why you shouldn't say it because every previous secretary of state has done so.

"Secondly, why on Earth have they not implemented Section 40 of the Crime and Courts Act 2013?

"It was a cross-party agreement, we'd love you to death. I'd hug you too if only you implemented these things."

Ms Bradley mockingly replied: "Oh my goodness, the promise of a hug from you is perhaps something that is difficult to resist."

READ MORE: Labour calls for part two of Leveson inquiry

She added to Mr Bryant: "You will know from my previous time in government that I always listen to victims of crime, I always make sure they're heard, I always make sure their voices are heard and I take note of everything they say."