Top Institutes providing this course are:
Lovely Professional University
LSR, New Delhi
Loyola College, Chennai
Christ University, Bangalore
Miranda House, New Delhi
Hindu College, New Delhi

Here are some of the colleges name you can prefer for M.A English.

Delhi University 

Jadavpur University

Presidency University 

Hyderabad Central University

Loyola College, Chennai

Admission procedure varies college to college so if you specify any college name then I can help you more.

You can consider below names -

1. Lady Shri Ram College (LSR) for Women, New Delhi

2. St. Stephen's College, New Delhi

3. Christ University, Bangalore

4. Loyola College, Chennai

5. Miranda House, New Delhi

6. Hansraj College, Delhi

7. Madras Christian College (MCC), Chennai

8. Hindu College, New Delhi

9. Sri Ram College of Commerce(SRCC), Delhi

10. Fergusson College - Pune

11. Ramjas College - Delhi

12. Indraprastha College for women - Delhi

13. Stella Maris College - Chennai

14. Sri Venkateswara College - Delhi

15. St.Xavier's College - Ahmedabad

16. Jesus & Mary College (JMC) - Delhi

17. St. Francis College for Women - Hyderabad

18. K J Somaiya College of Arts & Commerce - Mumbai

19. Mount Carmel College - Bangalore

20. Women’s Christian College - Chennai etc.

Hope this helps!!!