He is said to have described Kim Medcalf, who plays Sam Mitchell, as 'thick' and called Wendy Richard, who plays Pauline Fowler, 'one of the worst w******'.
He also allegedly called one of the show's most popular actors, Shane Richie, 'big-headed' and pregnant Jessie Wallace, who plays Kat Slater, was branded a 'vile dog'.
In his apology, Grantham said: 'I am wholeheartedly ashamed of my behaviour and feel that I have let down my colleagues, as well as my friends and family.'
However, other stars are still giving him the cold shoulder.
It was the second scandal to have hit Grantham this year. In March, a woman claimed to have been his mistress and he issued an apology to his wife and sons.