Hey I have 8 years of pure HR experience, in South Asia. Almost 5 of which is in a HRBP role.

I have a pretty good and diverse experience, but now I want to switch and move to business side of things.

I want to get a foot in consultancy post MBA, preferably in Europe, but am open to other locations as well.

Which business schools that offer MBA's are well know for placements into consultancies or for career pivots post graduation?

Consulting is a big field. Unless there's something else we don't know about you, you probably won't get into strategy consulting in Europe from an MBA there. Take a look at  https://find-mba.com/lists/top-business-schools-for-consulting and the FT ranking. Also see:
GMAT Tiers - strong schools for your GMAT www.find-mba.com/board/27082

Best MBAs for international students' placement http://www.find-mba.com/board/41143
Do you need to speak the local language? www.find-mba.com/board/34713

I did BP (Business Partner) roles in IT for many years and these kinds of roles can give broad exposure in different ways and often with senior stakeholders. 

The IT BP role lends itself well to a consulting career path, HR I'm not so sure though. I've worked with HR BPs in several organisations and used to be a member of a large BP community but haven't come across many who switched from HR to consulting.

Have a think about some specific consulting areas you could perhaps transition to. With the rise of AI, workforce transformation/optimisation and talent management strategy are hot topics at the moment. Perhaps look at the Big 4 consultancies' websites for details on their service offerings to help you define what kind of consulting you want to go into. Some of these are more on the business transformation side which could be a good area to aim for. 

There is a large body of evidence that many business transformations fail due to people and cultural issues and not technology and process which is where most investment is made.

[Edited by aslamo on Aug 31, 2023]

Although I am not an expert, I guess INSEAD, LSE, and Imperial will help you get a role in the consulting field.