I obtained an MBA from a prestigious university in London in 1999 and have this year completed an MSc Programme in Project Management based on the construction industry.My background has always been in support services i.e. PA, Office Management, Office Administration. I would like to get into consultancy but am faced with rejection everywhere I apply with the excuse of no experience. Can someone advise please?

You need to work your way up into either a senior management role in office management, or a professional role, before you move to consulting. It sounds like your best option would be the former.My concern, looking at your CV, would be the pace of your growth and learning. If you did your MBA in 1999, I'd expect you to have achieved more by this stage in your career. I suspect the same is true of the recruiters rejecting your application.It may seem unfair, but based on the information to hand, it isn't apparent that you used to working at an appropriate pace, or demonstrating the appropriate calibre to succeed in a consulting role.