Born out of the former British empire, the voluntary organisation focuses on development and democracy, but is turning its attention to boosting trade.
"However, there may also be important opportunities for the UK in the post-Brexit period to... negotiate new bilateral trade agreements with interested Commonwealth members."
The summit proper is on Thursday and Friday but kicks off today with three days of forums and events that lay the groundwork.
"A lot of that is going to be on the table at the Commonwealth summit," he said yesterday.
When Britain joined the European Economic Community in 1973, it sidelined historic trading links with its former empire, causing much hurt in some countries.
Britain is due to leave the EU in March 2019. A transition period runs until the end of 2020 after which the UK will be out of the European single market and customs union.
Britain is gearing up to strike its own trade deals outside the single market and is looking to its former global network.
Overall, the EU accounts for nearly half of Britain's trade; the Commonwealth accounts for a tenth.
"The notion that it can pick up the slack when the UK leaves the EU is nonsense."
Given its highly diverse membership, if agreements can be struck within the Commonwealth, they can likely achieve wider support.
The theme this time is "Towards a Common Future". The group is hoping to agree an ocean governance charter, a connectivity agenda for trade and investment, and a declaration on tackling cyber crime.
"CHOGM 2018 promises to deliver transformational change for the people of the Commonwealth," said the organisation's Secretary-General Patricia Scotland.
"Immediate impact combined with wider influence make the Commonwealth an unparallelled force for building understanding and cooperation towards realising global goals for social and political progress, inclusive prosperity, and sustainable development."
The summit comes immediately after the 2018 quadrennial Commonwealth Games on Australia's Gold Coast. Britain last hosted CHOGM in 1997 and is laying on the style. Queen Elizabeth II, the Head of the Commonwealth, is hosting a dinner for the leaders at Buckingham Palace in London.
On Friday, they gather in private at Windsor Castle, west of the city.
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