Is an MBA the best way to break in to PE from a pension fund?

Hi all

I know there are lots of posts on this specific topic but I wanted to get some views on my current situation.

I currently work for a UK corporate pension fund in alternatives investments and am moving to a new role as a Portfolio Manager at another pension fund (total 6.5 years of experience starting off in investment consulting and moving to in-house investment roles through a life insurance firm and now on the pension fund side). However, the role is heavily fund research based, making allocations to managers within specific asset classes (special sits, real assets, private credit, private equity etc).

I want to break into direct PE and get involved on the transaction side but have no relevant IB / M&A / PE deal specific experience. I note from other forum posts that having no PE experience pre-MBA makes this very challenging and so a potential route would be MBB or IB after the MBA for 2 years and then try and move to a smaller PE shop rather than the big funds necessarily, which I'm fine with if it means I can break into PE.

Would an MBA be the best way and if so would it be possible through LBS, Imperial, Said, Judge or Warwick? I would be open to INSEAD too but not really sure the US for b-school makes sense as I am currently in London and would want to stay in London for work.

TIA for any advice.