Continentel Europe undergraduate to equity research London

Hi everyone,

I'm an undergraduate math/physics student in continental Europe who's interested in entering equity research in London. What's the best part forward for me? It seems difficult to land directly into the position I want from my non target undergraduate. Would a Master in Finance such as LSE/LBS/HEC/Bocconi/Essec be a good idea? How do recruiters view a math/physics degree compared to econ/business? What's the most valuable practical experience I can gather? I've heard a Big 4 Valuation internship is a good start. 

To summarize most of my questions into one: What's the best things I can do to increase my recruitment odds?

I really appreciate any help in answering some of my many questions. I unfortunately couldn't find much information applicable to my situation.