This is going to take a while, so here’s the summary.
APM is applying to a Royal Charter
PMI(r), objected at that time
The Privy Council decided to recommend a Royal Charter for APM
PMI faces legal challenges
The High Court conducted a judicial review of the objections
PMI’s objections were dismissed.

If you want to know more, keep reading.
How did we get to this point?
APM announced in 2007 that it would be Chartered for project management. APM explains the reasons as follows:
It is a UK charity that acts for the public good and is committed to gaining Chartered status for the project management profession in the UK. This will ensure recognition, status, and higher standards for the profession in a time when the UK is more urgently in need of effective and efficient project delivery and sponsorship.
PMI filed an objection to APM being granted Chartered status. This started a long process for judicial review. The results were announced on Thursday.
Why did PMI object to the proposal?
I’ve searched the internet for an explanation, but I cannot find the original email that was sent to members by PMI UK on June 9, 2012. It explains these reasons.
APM must have been approved by the Privy Council as representing most of the project management profession in order to be granted Chartered status. APM’s Chartered status would mean that it represents only the vast majority of UK project managers. PMI, which has over 6000 members and many credential holders, also represents a substantial number of UK project managers. The Chapter’s management team expressed concern at the Privy Council’s failure to consider that APM cannot claim to represent all of the profession due to PMI’s large UK membership.
Diversity in the market for project management tools and qualifications is in the public’s best interest.
The diversity of approaches available to project management in the UK is a benefit for the profession. PMI has a million members from 185 countries. This gives its UK members a unique perspective on project management that APM cannot duplicate.
The Charter application process did not take into account the views and opinions of all project managers, especially those who use the global approach advocated by PMI.
The first point is especially important. The Minister of State at Department for Business Innovation and Skills, in 2009, informed the Privy Council Office of his decision not to grant APM Chartered status. He felt that APM didn’t meet the criteria.
A Charter can only be granted if there is unanimous agreement. APM’s application was rescheduled after it was unable to reach a unanimous decision without the support of the Department of Business Innovation and Skills.
What happened then?
APM did some lobbying. The government changed, new officials were appointed, the departments involved were reorganized, and a new person looked at the evidence. The Department for Business Innovation and Skills retracted its objection in 2011.
PMI’s concern about the Royal Charter resulting in an anti-competitive edge for APM members was rejected. APM and PMI compete for memberships and fees. However, the representative of the Office of Government Commerce stated that it would be in the public’s interest for APM to be granted Chartered status.
Both organizations can be joined.
APM is the UK’s largest professional organization in project management.
APM members are not eligible to be called Chartered Project Professionals.

With unanimous approval now in the cards, A

APM Chartered status is now: PMI’s objections have been dismissed