The Queen has welcomed leaders to “my own home”, Buckingham Palace, as she hosts the Commonwealth Heads of Government Meeting (CHOGM).
She told the gathering of dignitaries, royals and the PM that the Commonwealth was “growing stronger year by year”.
Issues under discussion at the two-day summit include ocean conservation, cyber security, trade and the Queen’s successor as head of the Commonwealth.
Theresa May said the issue of plastic waste would be central to the agenda.
Welcoming the leaders in the palace ballroom, the Queen said it was a “pleasure, this time, to welcome you to my home” for the bi-annual meeting in London.
She said the Commonwealth was “one of the world’s great convening powers” as she spoke of protecting shared ocean resources and trade between the countries.
The Queen also said it was her “sincere wish” that the Commonwealth would continue to “offer stability and continuity to future generations, and will decide that one day the Prince of Wales should carry on the important work started by my father in 1949”.
A decision on whether Prince Charles will succeed her as head of the Commonwealth is expected from the heads of state on Friday, No 10 has said.
Mrs May told the leaders the summit would “take on some of the 21st Century’s biggest questions”.
She said: “There have been difficulties, successes, controversies, but I believe wholeheartedly in the good that the Commonwealth can do.”
The prime minister thanked the Queen for hosting the event, calling the monarch a “steadfast and fervent champion” of the Commonwealth.
The ceremony was attended by 46 Commonwealth heads of government, out of the 53 member states, with the remaining attendees being foreign ministers.
Prince Charles told attendees the modern Commonwealth had a “vital role to play”, adding: “I pray that this [meeting] will not only revitalise the bonds between our countries, but will also give the Commonwealth a renewed relevance to all its citizens.”
Camilla, Duchess of Cornwall, Prince Harry and Prince William are among the other royals attending the opening ceremony.
The Commonwealth represents about 2.4bn people, but critics say the organisation is so disparate that it struggles to know what it is for, says BBC royal correspondent Jonny Dymond.
Theresa May said she would be “rallying” Commonwealth countries to follow the UK’s fight against marine plastics – which has included a ban on microbeads and proposals to introduce a deposit return scheme for drinks containers in England.
“The Commonwealth is a unique organisation, with a huge diversity of wildlife, environments and coastlines,” she said.
The UK is due to consult on proposals to ban plastic straws and cotton buds – 8.5bn of which are thrown away in the UK every year – as part of plans to tackle the issue.
It comes as 60 UK music festivals, including Bestival in Dorset and Boomtown in Hampshire, also pledged to ban plastic straws at their events this summer.
Foreign Secretary Boris Johnson has said he will raise LGBT rights with leaders of Commonwealth nations on the fringes of the meeting.
As head of the Commonwealth, the Queen presides over the meeting but does not take part in the leaders’ discussions.