David Cameron under pressure to reveal all messages exchanged with Rebekah Brooks

British Prime minister David Cameron is facing calls to publish up to 150 secret e-mails and text messages exchanged with former News International executive Rebekah Brooks.

Earlier it emerged that Cameron had sent Brooks a text about a "fast, unpredictable ride" on her husband's horse, and that she told him in another text that she "cried twice" during one of his speeches.

The two new messages, leaked to a Sunday newspaper, had been provided by Brooks to the Leveson Inquiry as part of its investigation into the relationship between the press and politicians.

According to the Telegraph, nearly 150 messages held by Downing Street have not been published because they were deemed not "relevant".

UK politicians, however, called for more transparency about Cameron's friendship with Brooks, who is currently awaiting trial on charges related to News of the World phone-hacking scandal.

Lord Oakeshott, a senior Liberal Democrat, said publication was "clearly" in the public interest.

"These exchanges show an unhealthily close relationship between David Cameron and Rebekah Brooks," the paper quoted Oakeshott, as saying.

"Prospective prime ministers must not appear to be hand in glove with chief executives of vast media groups," he added.

According to the paper, Cameron ordered the setting up of the Leveson Inquiry following disclosures about phone-hacking, and since then, his friendship with Brooks has been under close scrutiny.