Hi MB D.C.
I agree with firesafety that the simple answer is YES.
CDM Reg 6 (forget the waffle in the guidance in L153 and focus on what the Regulations actually say!)
Regulation 8 General duties
(1) A designer (including a principal designer) or contractor (including a principal contractor) appointed to work on a project must have the skills, knowledge
and experience and, if they are an organisation, the organisational capability,
necessary to fulfil the role that they are appointed to undertake, in a manner that
secures the health and safety of any person affected by the project.
(2) A designer or contractor must not accept an appointment to a project
unless they fulfil the conditions in paragraph (1).
(3) A person who is responsible for appointing a designer or contractor to
carry out work on a project must take reasonable steps to satisfy themselves that
the designer or contractor fulfils the conditions in paragraph (1). ....CONTINUES....
So, it is a two way process. Prohibition accepting an appointment if without the skills, knowledge and experience (SKE) and, where relevant, organisational capability BUT also prohibition on the person (e.g. Client) making the appointment unless the appointee has those qualities.
For reasons alluded to in firesafety's response, HSE decided to move away from a requirement for "competence" in CDM 1994 and 2007 in favour of SKE etc in CDM 2015. Why this means anything other than "competence" I have never worked out! - some assume that a more complicated form of wording was largely influenced by politics.
A Client may have entirely legitimate reasons not to rely only on a potential appointee being able to tick one or more of the various accreditation schemes.
One of the benefits of the previous legislation is that CDM 2007 came with an Approved Code of Practice and guidance which included baseline questions to ask about the competence of an organisation or specific individuals who might be working on a project.
Unless the situation has changed very recently you can still download that guidance L144 from the HSENI website. In my work, we still advised our Clients to use the questions published by HSE as their starting point for checking on SKE etc, though in some cases with some bespoke adjustments.