Evercore/Greenhill london through networking

I'm a master student applying for SA in London.
I would like to apply to boutiques like Evercore, Moelis, Centerview, Qatalyst, Greenhill.

These are not well known in London as they are in the US, and I believe my best bet to get past CV screening would be getting a personal referral from one of their current analysts.

I am thinking of contacting these 1st year analysts with a message on Linkedin. (they are not alumni, unfortunately, so I'd cast a wide net)

But should I play vaue in the first message and ask them for a skype call/grab a coffee?
Or should I make clear I'm interested in their company and ask for their help from the first message?

I have read the various cold-emailing posts here on WSO. What do you think is the best way given my situation?

Thanks in advanace.