The 27-year-old Everton left-back got the nod ahead of Cole, who is still seeking his 99th cap.
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Now Baines has told reporters that he will make it hard for Cole to edge his way back into the starting eleven: "Ashley is a terrific player but in the games I've played I've shown I can come in and do a job as well.
"Of course you want to play more. All I can do is play as well as I can for Everton, and that's all I'm focused on.
"I'll just keep playing as well as I can."
England's World Cup 2014 qualifying campaign has begun well, with Roy Hodgson's men taking seven points from a possible nine and topping their group.
England travel to Poland on Tuesday looking to continue building upon their impressive start in the qualifying stages.