from my experience (I had a few offers and a few declines when I applied for PhD but they were all for funded places), you'd hear from them within 2-3 weeks after interview. If there was an application deadline, and if you were shortlisted, you'd be invited for an interview within 2-3 weeks after the closing date. Some of my self-funded friends didn't have to sit any interviews, they were given places straight away, about a week or two after submitting application.
Good luck with your applications.