Can I use my university email address for job applications? I just started a postdoc position in England, but I have a personal problem with the place. I want to apply for another postdoc position in other cities.

Am I officially allowed to use the university email to contact other professors for finding possible postdoc position? Because, it is not an official use related to my job, but personal.

I wish to use my university email, as it can attract more attention, as I am already working in England. Many Indians send email to professors, and they do not read them carefully.
I, personally, wouldn't use anything else.  This might depend a little on the culture of your field (see Should I use my university&#39;s letterhead for a cover letter for a job application? for a similar discussion), but exactly as you say, using your professional email address might well cause someone to give your email an extra second of attention.