DAVID Cameron is facing fresh embarrassment over playful text message exchanges with Rebekah Brooks as calls for full disclosure intensify, with claims 150 exchanges have not been seen by Lord Justice Leveson.

With the judge's report due to be published this month, two more messages from 2009 between the Prime Minister and the former tabloid editor and News International chief executive have been revealed.

In one, Brooks, facing trial over the phone-hacking scandal, texted Mr Cameron following his 2009 party conference address . She wrote: "Brilliant speech. I cried twice. Will love 'working together'." In another text, the PM, referring to Brooks's racehorse trainer husband Charlie, wrote: "The horse CB put me on. Fast, unpredictable and hard to control but fun. DC."

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The exchanges are supposedly part of a cache handed to the Leveson media standards inquiry. Very few have so far been made public, sparking accusations they are being covered up. Brooks told the Leveson Inquiry Mr Cameron signed some of his messages to her "LOL", mistakenly thinking it meant "lots of love" rather than "laugh out loud".

She said that at the height of the phone-hacking scandal in 2010 he sent a message through an intermediary urging her to "keep your head up" and expressed his regret he could not be more loyal in public. Lord Justice Leveson is believed to have received a large amount of correspondence from the Prime Minister, Brooks and former Downing Street communications chief Andy Coulson.

Labour frontbencher Chris Bryant has called for all the material to be published, suggesting some was being withheld because it was "too salacious and embarrassing".

Yesterday, he said: "I'm told there's a stash of about 130, 150 texts and emails which have not gone to Leveson, which have not been shown to anyone, have been reviewed by an expensive lawyer. It's about time that we all saw it."

A Downing Street spokesman said: "The Prime Minister has always been happy to comply with Lord Justice Leveson."