No Offer, out of school - What to do

Hi everyone,

EU student here just graduated from top target UK masters.

I just finished my internship at a strong volume shop in London, however, despite my work being continuously praised by the people I was closer with and my VP and director hitting me up on my personal to thank for the help and offering to serve as a reference, ultimately the group head decided to not give me an offer due to headcount (intern class was overall very strong) citing performance on my final intern presentation. 

Was wondering whether this situation would impact London off-cycle and FT recruiting to the extent that I'd have to go back working in my home country. Unfortunately I did not get a Graduate Visa (looking back a big mistake) so a UK firm would have to sponsor me as well. If I was dead set on staying in the UK, how would you frame the no offer situation, and would networking/cold emailing help in gaining advantage? (especially as in LDN it carries less weight than in the US?)

Any help or relevant anecdotes appreciated