Career advice for investment banking, or similar

I've been working at a bulge bracket firm for around 5 years in the back office in a temporary job, in a sort of marketing related role. I graduated with a BA (2.1) in Philosophy in 2012, from a little known university in London.
I wanted to get a front office analyst job, so I did a Postgraduate Diploma in Accounting and Finance at the London School of Economics. I had to continue working full time in the same job, during the 9 month period I was studying (to afford tuition), so I didn't have much time to apply for internships.
Also, even though my grades at the Finance and Accounting homework were straight As, I got lower grades in the exams (because I was working, I didn't have time to memorise all the formulas. But if I could look them up in a book like I did for homework, I would have got As).
After graduating, I talked to the career advisor at LSE. There I was told, because the grades were low, there's no chance at investment banks, and that I should think about trying for an internship in insurance. I didn't do that.
It's been around 3 years since graduating, and I'm still working in the back office in the same temporary job. Because the firm is going through general cost cuts (which have been in the newspaper, everyone knows about it), I'm sure they will not be promoting anyone at all - so no chance of climbing the ladder in the back office at all.
Do you think there are any chances of getting accepted at a job even remotely resembling an investment banking analyst in London? (even a smaller firm, or not even investment banking)