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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Sunny this evening, then dry overnight. There is the risk of thundery showers for Kent tomorrow morning, then sunny spells by the afternoon
Sunshine to end the day then dry tonight. Tomorrow will be mostly dry and feeling fresher with the risk of a heavy shower in the afternoon
The video, obtained by ITV News, shows scores of migrants desperately trying to board lorries in a restricted area within the tunnel.