MS Finance - Profile Evaluation

Hey Guys, I decided to post here as I figured I could get some good advice here.

I want to apply for a MS in finance between the UK and USA. My top choices in the UK are LSE, LBS and Oxford. The second tier would be CASS, UCL and Imperial. In regards to the US, my top choices are MIT and Princeton (far reach), I am still looking for other programs that are good fit. I would like to know what my odds are and how competitive I am.

Education:
BEng Mechanical Engineering - City University of London ( Non Target) with a First class Honours (70.8%). Equivalent to 4.0 GPA in the states.
I have not taken the GRE yet, but it seems like I'll get 165+ in the quant and 155+ in verbal.

Work Experience:
1 year internship with Procter and Gamble in Product Supply ( Not related to finance in any ways/ regret doing it)

I have a gap year between now and when I want to start my Masters. I am working on getting off cycle internships in the USA in financial fields, more specifically buy side. I am working as well on the CFA. I hope to get level 1 in December and level 2 in June.

Any advice would be appreciated.