You have got a lot great company names on your CV. If you would like to continue pursuing digital work, digital arms of the consulting firms e.g. BCG Digital Venture or McK Digital would love to have someone with such extensive and very relevant experience. Potentially opportunities could be either Product roles, or Venture Architect (more biz driven) roles.
In the digital arms, you would definitely have chance to work alongside the consultants on projects that has a digital component (in some cases might be the key component).
However, if you want to join the traditional consulting track i.e. the generalist, it would be more challenging given your background and experience seems more on Product/Tech so far. You won't be playing to your current strengths, but need to build new skills and business acumen. Just trying to give you the realistic picture here.
What's more, you also need to understand that the traditional consulting roles work in a different way from the digital arms (even though the gaps are probably closing, but still quite some differences). You need to consider the sub-culture, way of working etc. E.g. if you are sent to a remote jungle to work in pulp and paper manufacturing plants to fix their operational issues like machinary maintennace or shift planning for 6 months (this is my real experience), while most of the client operation teams are only high-school educated, are you okay with that?