What if PhD application date is closed? I sent an e-mail to a professor along with my CV explaining my research background and expressing an interest in joining his research group as he has asked to send CVs if anyone is interested in joining his group. After a few hours, I got a reply from him saying that my research background is quite relevant to his. He has also encouraged me to apply to the college and take the English tests.

When I checked the college website, it seems that the interview date for the possible candidates has already passed and they have stopped taking further applications. 

I haven't yet taken the English exams as well. What should I do? Shall I send an application anyway? Is there a chance for me to get the scholarship?
If someone has told you they are interested and to do it, where is the doubt? I say do it. 

You can always send the professor an email saying that you have seen that the application deadline is over, and ask if they think you should still apply. 

A lot of PhD offers have no academic deadline other than the funding deadline, very often you can just start whenever.