Once upon a time, I knew about the British School of Languages, which were doing a good job. They had branches all around. As I do not know how good they are today, I would advise you to do a li'l research focusing on this.
The British Council focuses on language development.
The Delhi Centre, for sure, does training on language improvement.
This is the link to Mumbai Centre.
Please see if they can be of help. There must be many quacks who offer instant solutions. But, I guess it takes a while to refine your linguistic skills and these guys at the British Council, will help you to have a strong foundation.
As far as your sentence is concerned, I would refine it and re-write it in the following manner:
Is any one can tell me is there any good institute in Mumbai where I can join and improve english in one month.
Please let us know
"Can anyone suggest a good Institute in Mumbai where I can improve my English (linguistic skills) within a month?"
From India, Delhi