From everything I have read in this thread, I sense an obvious sense of frustration but also a lack of appreciation for what you actually have.
I saw something you said about "Every other grad can get a good job based on their degree" (or something to that effect), which is completely untrue. My sister graduated nearly 3 years ago, (coincidentally also from Cardiff), and has yet to find any job based on her degree. She is currently in some temporary office job that has no relation to her aspirations, because TIMES ARE HARD. Many other people are in your situation - you are not the only one!
In terms of the job you've been offered now, £6.41 p/h isn't the minimum wage. £6.19 is the minimum wage, so this job of yours isn't the minimum wage at all. I was in a job a year ago that paid below the minimum wage because it was all I could get. I asked myself the question, "What would I rather be doing?" The two answers were, 1) Sit around moping or 2) Actually do something about it and I chose option 2. You should do the same.
The jobs market is ridiculous at the moment, because we live in 2013 and there is a tight squeeze on literally everything. Stop thinking you're entitled to a dream job because you went to university, stop moaning and bloody get on with it!