Decide if there is a problem.
Have a discussion.
Appoint a committee
Appoint a committee to appoint the committee.
Establish fair remuneration starting with the chair of the appointments committee. Say £100,000 plus expenses. Plus offices. Plus staff. Then a deputy chair. £95,000, plus expenses, plus office, plus staff. The chair will need an official car at this point. Then an Assistant chair. £85,000, plus expenses. Plus office. Plus staff. Sadly, the only suitable nominee is already on another committee where he is paid £150,000 and wants an improvement. So, £180,000 for the Assistant chair, £190,000 for the deputy chair, £200,000 for the chair.
And so on and so on.
10 years down the line, hire the cheapest builder imaginable who will botch the job.
5 years later, the whole process needs to begin again.
That's the British way.