Sir Jeffrey was joined on the council by former DUP leaders and Northern Ireland First Ministers Peter Robinson and Dame Arlene Foster, former DUP deputy leader and peer Lord Dodds, and the region’s Lady Chief Justice Dame Siobhan Keegan.
The council, made up of members of the Privy Council, met at St James’s Palace in London on Saturday to formally proclaim the new sovereign, proceedings that were televised for the first time.
Sir Jeffrey said: “It was a great honour for my colleagues and I to participate in the Accession Council.
“We recognise this is a momentous and historic moment for the United Kingdom.
“In one sense we are all deeply saddened by the passing of Her Majesty the Queen and the members of the Privy Council gathered at St James’ Palace this morning, we were very mindful of the enormous contribution she has made as our head of state over many years.
“But the council was also looking to the future and proclaiming the new King Charles III as our head of state.”
He added: “Whilst this may seem to be a formality, it is a very important act of the Privy Council in law and it gives effect to the reign of our new monarch.
“The proclamation will now be announced in each part of the United Kingdom and it is expected that the proclamation will be made at Hillsborough Castle tomorrow as well as in Edinburgh, Cardiff and London.”