Bosses on the ITV2 show are said to have issued the warning after TOWIE favourites were photographed on nights out in London with their rivals.
Bright told The Sun: "The Made in Chelsea lot are lovely, I've met them a few times, but we just can't. We all had a text message saying we can't be in a picture with anyone from the other show."
The publication alleges that the TOWIE cast even refused to participate in a group photo with the Made In Chelsea team at charity bash earlier this week.
TOWIE producers Ruth Wrigley and Tony Wood blasted Made In Chelsea during the Edinburgh TV Festival in August.
"What it lacked was humour and it was shot upfront so we knew where it was going," Wrigley said, with Wood adding: "I think Chelsea lacks the entertainment part of the thought process."
> 'TOWIE', 'Made In Chelsea' party in London - pictures