It's less about qualifications, though if you're a graduate I'd suggest you do a postgrad course: Cardiff is widely held to be among the best. It's more about luck, contacts and persistence.
I'd suggest you approach your local paper and offer to write for them on a freelance basis - suggest you do something like game reviews for them if they don't already do them. Ask if you can do work experience there, and at your local BBC radio station if there is one.
Publishing on the web is one thing, but what really counts is where your stuff is published. I suppose a really elegant blog would not count against you, but random bits of writing for websites that nobody's heard of won't help you. If you managed to get stuff on a mainstream website that would help.
Have a look at the NUJ website which should have some links worth reading.