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Summer Internships...do I stand a chance?

P.C2001

A bit of background info:
-A*AAA at A Level (underperformed my predictions/expectations and these results were average for my school)
-3rd year Economics at LSE
-Hold a senior position within the SU
-Limited experience as a Finance Intern at a local firm

I'm beginning to become concerned because I was very late to IB (didn't know what a spring week was at the time) and committed the cardinal sin of applying just before all the summer internship deadlines last year, and didn't get one. This year I have been rejected at first stage within half a week by JPM and MS despite spending days on each application. I know these are the very top employers but I am worried if the fact I applied last year will harm me throughout my applications?

Thanks for any help/advice in advance