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For what it's worth, OP, I graduated with a BA and MA (which I paid for) in English Literature and I'm now 28, working in a pretty good job. I'm definitely not in the type of long-term career I want to be in, but it's an above-average salary for my area. More importantly, the experiences I've had over the past few years have been invaluable.
It's a fucked up system, but applying for jobs and getting hired is very much about tailoring applications, jumping through hoops, and dogged perseverance.
I won't try to offer advice, but I will tell you how things came together for me: I worked a load of various temporary jobs while doing my MA to pay off my loan. As I paid down my debt, I signed up to one of the better agencies handling healthcare admin around my hometown. While there, I was smashing out applications for permanent positions left, right and centre. I interviewed for a part-time permanent NHS job, landed it due to one of the doctors liking the cut of my jib, and stayed there for about two years. I earned a pittance but it looked fantastic on my CV. During this time I was in constant contact with my old university careers advisor, who put me in contact with a place doing private healthcare I.T. type work. After two interviews there, I'm now on a decent full-time wage.
These things tend to compound, one thing after another, step by step. The above probably isn't unusual, but it's not a typical 'grad job' route, either. No one expects you to stack shelves forever.