Imperial/LSE/ Msc Finance?

I’m a recent grad from a UK low target/semi target school (UCL/Warwick/Durham) and studied a non-STEM/Finance/Econ degree (think, History/Law/Politics) and got a 2.1. I’ve completed a WM internship at a large balance sheet bank and have been working in private banking at a bank in my home country for 4 months (think Aus/Canada/HK etc). I also have an off-cycle at a LMM PE firm lined up for later this summer (non-convertible).
 
I have just received acceptance from Imperial’s MiM alongside LSE’s Msc Financial History. Goals are anything within finance, consulting, capital markets, research etc. Looking through LinkedIn it appears Imperial’s program is a feeder for consulting, less so for banking/finance. Does anyone have any experience in this program and can speak to the recruitment outcomes? Is my background competitive if I go via Imperial? What about if I take the program at LSE?
 
Also, I have considered taking the year to instead do the GMAT and (hopefully) accumulate more off-cycle internships, hopefully to a) get into a better program and b) get some IB exp on my resume before re-applying to SAs. However, I’m not sure if this is the right move, as I’ve yet to see anyone from a non-STEM/Finance/Econ background with a 2.1 get into LSE’s , Ox, or Imperial’s flagship Msc Finance, instead LSE/Imperial’s Msc Finance & Accounting instead. LBS would probably be my target in that case.
 
TLDR; Essentially, which of Imperial’s MiM or LSE Msc Financial History is better for my goals? Can I yield an IB/Consulting/Cap Markets etc SA position from Imperial? Should I reapply to better programs next year with a strong GMAT?
 
Cheers