Finance Master's Univeristy Choice

Hello everybody,
I am here simply for advice.
My case:I am in my second year in a three year course studying towards a bachelor's in Finance and Management.I am in a Russel Group university (UK) however it is far from what I am aiming at.
My question:I am looking forward to excelling my resume/knowledge/employability by getting a master's in a top university.My question is expect for aiming at first class/involve in extra activities/take GMAT in the summer what would you recommend to get a better chance and compensate the lower ranking of my current university (by top university I mean-LBS,LSE,Imperial,Bocconi,HEC,MIT Sloan etc.)
Apologises,for the generic question but I believe that there are people here in similar position who can share useful thoughts.

P.S. I would also really appreciate anybody recommending employers who open positions for internships late or do not consider applications on rolling basis (as a few employers already rejected me for spaces being full).

Regards,

K