The judge, 33, let slip racy show secrets as she became increasingly tipsy during the interview.
She said: "Everyone is really frisky on the show, everybody is horny. The year I was a contestant, everyone was just really gagging for it."
Alesha's Strictly co-stars Bruno Tonioli and Craig Revel Horwood were stunned at the leggy star's outbursts, with Tonioli, 56, grabbing the bottle and saying: "No more drink for Alesha!"
Alan was enjoying every moment, declaring "This is chat show gold" before rushing to pour her another glass.
But Alesha was quick off the mark, yelping: "Give me the bottle!"Tucking in ... Alesha glugs wine from the bottle to the amusement of Bruno and Craig
She then continued: "As I was saying, you spend eight hours a day rubbing up next to each other. Of course you're going to get a bit frisky."
Alan then asked: "Is it true the better dancer you are the better you are in bed?
Alesha laughed: "I should think so, Alan."
The giddy star also called show fan the Duchess of Cornwall a "Strictly stalker" before moving on to the subject of rival telly show The X Factor.
She said: "I don't understand what all the fuss is about, why can't we just enjoy both shows.
"I actually don't think the public give a s***. The public will just Sky Plus one and watch it later, they don't care."
But she then took the opportunity to have a pop at the ITV1 show, saying: "The problem is Al, they focus too much on the drama, and everything else other than the singing."
Alan responded: "At this point you've crossed the line from a fun drunk to a violent one."
Alesha giggled and added: "You know what it is, I feel like I'm at home with my mates, having a gossip."
The star later appeared to be a little ashamed of her antics. She tweeted: "Apologies for being pickled on Alan Carr! I did have fun though! I am officially a lightweight and clearly a cheap date!!!"