Yes, there are English graduates who got into IIM Ahmedabad, Bangalore, or Calcutta. Although the number of such people is less. If you are an English graduate, you will be at an advantage. As your profile will add diversity to the batch. If you can manage to score well in CAT and have a stellar academic background, you can get calls from IIM ABC.
It is essential to note that although the number of students from the said background is very minimal, it is not uncommon or impossible to get admissions. This also does not imply that Engineering students are given extra preference.
While students need not be worried about their graduation background as much, just be sure to prepare really well and get high scores in their CAT examination to ensure that they have the relevant academic expertise to back student diversity and seek admissions at IITA.