The Leveson Inquiry asked David Cameron for communications between himself and representatives of News International that covered a “range of issues” that went further than just the BSkyB bid, The Independent has been told. However, lawyers advising the Prime Minister “interpreted” the request for information as narrowly as possible, allowing him to hand over no texts or emails to Lord Justice Leveson's press inquiry.

The inquiry's decision to allow Downing Street lawyers to "interpret" their requests, and to leave Mr Cameron to define for himself what "inappropriate conversations" meant, was last night criticised by the Labour's shadow Justice Minister, Chris Bryant. The Rhonda MP has been demanding for weeks that the Prime Minister publish "dozens" of emails described as "embarrassing and salacious" between himself and the former chief executive of News International, Rebekah Brooks.

The Independent revealed the existence of the emails last month. Legal advice on the emails that Downing St received from government lawyers said that full disclosure to Leveson was not necessary because they fell outside the remit of the inquiry.

"There is a clear disconnect between what Leveson asked for, and the interpretation Downing Street put on that," Mr Bryant said. "To resolve this, the Leveson Inquiry should now publish the exact questions it put to the Prime Minister."

Mr Cameron has repeatedly refused to answer calls by Mr Bryant in the Commons to publish the private emails between himself and Mrs Brooks. He is also withholding emails between himself and the former News of the World editor, Andy Coulson. Mr Coulson later ran Downing Street's communications operation.

Downing Street has denied Mr Cameron is hiding anything, stating that everything they were asked for has been handed over. However, Leveson asking for communications that went beyond the BSkyB bid substantially weakens Mr Cameron's defence.

"The public does not know what the Leveson Inquiry asked the Prime Minister for. Neither do they know the scale of the communications between the PM and Rebekah Brooks. The number of texts and emails is crucial here," said Mr Bryant.

Robert Jay QC, the inquiry's senior counsel, repeatedly asked Mrs Brooks how often she had texted Mr Cameron. However, the emphasis on frequency was absent when the Prime Minister was questioned.

Mr Bryant has estimated that up to 150 text messages between Mr Cameron and Mrs Brooks were disclosed to the Leveson Inquiry by News International. None were handed over by Downing Street.

Two texts were discussed by the inquiry, with one mentioning that Mr Cameron often used the term LOL, which he thought meant "lots of love".

Last weekend two further texts held by the inquiry were leaked to the Mail on Sunday. Their content proved embarrassing for Mr Cameron, with Mrs Brooks saying she cried twice during a Cameron Tory conference speech, adding: "Will love 'working together'."