In one message obtained by the Mail on Sunday, the Prime Minister thanked Mrs Brooks for letting him ride one of her horses, joking it was "fast, unpredictable and hard to control but fun".
In another the journalist, who faces trial in connection with the phone hacking scandal, praised Mr Cameron's speech to Tory conference, saying: "I cried twice."
The playful texts are apparently part of a cache of texts and emails handed to Lord Justice Leveson's media standards inquiry.
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Hampshire police arrest seven more men in investigation into an alleged conspiracy to commit serious sexual offences on the Isle of Wight.