How to go about networking before FT recruiting (LDN)?

Hi,

I am interning at an EB this summer (PWP/Laz/PJT) in London but would like to keep my options open for FT as I am yet to experience a BB and am aware exits are stronger there.

How does FT recruiting in London work for say MS/JP/GS if you are a strong candidate and how should I go about networking with these firms?

I don't want the information that I am shopping around to become known to my EB but I am keen to make myself a strong candidate for FT so I am unsure if cold emailing etc is wise and would appreciate any tips/insight.

Thank you.