Masters after undergrad vs MBA after experience

Hi, I'm a college senior at UK semi-target (Russell Group) with exchange year completed at top target (Ivy League). Grades are alright: On track for first class and above 3.6 GPA. Back office summer intern at well-known prestigious Boutique. PE analyst internship at UMM PE shop. European Citizenship.

My ultimate goal is to work in NYC. Ideally IB. I suppose that I need a FT US degree to have a good chance. I heard internal transfers are difficult and take time.

US B-School Master programs are relatively new and still rare. While the options seem great (ex: Duke, Kellogg, MIT or Stern), many other top targets are not available without work experience (as far as I know, Wharton, Booth, or Harvard have no options for college seniors). MBA is the better degree, so it would make sense to wait. However, my current profile might not be strong enough to aim for the very top jobs and I might end up in something uninteresting until then.

Question: To break into Wall Street, would you recommend to pursue a US Master's now or work for a couple of years in London and aim for an MBA later?

Would greatly appreciate any feedback, thanks!