Advice for an uncertain graduate

Hi Guys,

I was seeking some advice as to how to go about getting onto the graduate scheme of BBs in corporate finance. I've previously had interviews for top Bulge Bracket IB SA positions in my ultimate year of university but was unfortunate to not achieve a place in one. I was massively under-confident in the interview. Mainly, I felt like I hadn't done the "necessary" legwork to feel I was worthy of a place there in the interview, across from a senior banker (I was achieving a middling 2:1 in my degree at that point and in 1st & 2nd year, only achieved a 2:2).
I recently however just graduated. My academic and professional credentials are the following:
- English "public" school, achieving top GCSE grades
- International school for IB (International Baccalaureate): admittedly didn't achieve such top grades thereafter
- Scottish Russell Group uni, achieving a 1st in Mechanical Engineering with class rank 5/27
- Have done 2 internships in Engineering, 1 in Advertising and 5 in finance, across a broad scope of areas (Project Finance, M&A advisory boutique and Private Equity firm in India and a boutique IB's sales & trading along with a Spring Insight week with a BB in London).
My question is this. Now that I've graduated, will it be held against me that I didn't get a Summer Analyst position if I apply for a full time graduate role? Or is it worth applying for a Masters in Finance from a brand name school (Oxford, Cambridge et. al.) and from there apply again?
Any advice would be much appreciated...