That's a big switch for those schools to help with. Investment Banking Front office might be a significant stretch from any of those schools.
Consulting would be easier although strategy consulting again would be difficult.
I'm not sure about Boston - but Manchester would likely help you better in getting into consultancy (utilising the internship) but their recruitment would be mostly into the big four professional services firms and then firms like Accenture, BT, Capgemini etc. Obviously Strategy consulting roles are in the minority in these so where the challenge lies.
ICL would be better for the Investment Banking route - given its in London and strong links to firms in the City - however the one year MBA would make the switch more difficult and without the prior experience, opportunities will be slim.
Looking at average salaries/rankings etc I'd say your opportunities from Boston would be slight worse than ICL and MBS.
If it was me in your shoes - I would try to make a career switch into the top strategy consultancies now utilising HR specialty as a experienced hire.
If that didn't work then consider MBS with a look to getting into big four strategy consulting.