Binky took to the social networking site this morning (21 May) after receiving a photo with the caption: "Me, [friend's name] and Alex Mytton chillin at Spencer's lol."
The reality star, who recently found out that Alex had cheated on her several times, shot back: "You should be really proud of yourselves."
Binky then ranted: "If any of the other skanks sends me pictures of them with Alex... Prepared to be taken down you low life skanks! You should be ashamed."
The girl who posted the picture has since disabled her Twitter account.
In Monday night's episode of MIC, Binky was told that Alex and Spencer had enjoyed an "orgy" with several girls, after Jamie Laing let slip the secret to Lucy Watson.
Mumbling Alex, who had finally admitted to cheating with two girls in the previous episode, said he "hooked up" with the women but couldn't remember if he'd actually slept with any of them.
Binky responded by giving him a whack around the head. There's no word yet on the state of play of their relationship, although Binky later admitted on Twitter that the slap had hurt her hand.
Meanwhile, Binky last night tweeted a picture of a suitcase as she prepares to film the MIC spin-off with some of her cast mates in New York.
Alongside the snap, Binky namechecked the suitcase makers before saying: "And the packing begins!!!! Thank you for my huge suitcase to hold 2 months of my life in NYC!!"
She then added a photo of her mum Jane, teasing: "All this packing is exhausting!!! ;) haha.... Thank you @MummyFelstead."