I applied online. The process took 6 days. I interviewed at Primark (Kingston upon Thames, England) in Feb 2014
Interview
3 Stages: Application online, phone screening and an interview in person. The application online was simple - basic personal information plus a CV and Cover letter. The phone screening took about 5 minutes - it's more to check if you can actually speak English. The interview itself is easy as long as you can show that you actually care.
Applied in September and heard back a week after about the interview which lasted around 20 minutes. Questions aren't too difficult if you do your research by reading reviews on Glassdoor. Staff were very friendly.
I applied online. The process took 2 weeks. I interviewed at Primark (Manchester, England) in Jun 2016
Interview
Applied online and filled in an online screening questionnaire, and said when I would be available. Soon afterwards (within a week I think) I got a phone call inviting me to an interview with the store manager.