The Duke and Duchess of Cambridge will remain committed to their core charitable themes when they become the Prince and Princess of Wales, an aide has said.

William is said to want to do things “the Cambridge way” following his Caribbean tour with Kate that saw the couple heavily criticised for images that smacked of “colonialism” but also welcomed with warmth by Caribbeans.

The visit is likely to be judged as a landmark moment for years to come – when the growing awareness of racial equality, in light of the Black Lives Matter movement, meant future Commonwealth tours would have to be sensitive to these issues.

The duke addressed the issue of slavery during a speech in Jamaica, denouncing it as “abhorrent” and saying “it should never have happened”.

Labour leader Sir Keir Starmer said William “could have gone further” in his comments but he acknowledged “it’s a difficult one”.

Sir Keir told LBC Radio: “I think that he may go further in the future.”

At the end of the tour, an aide said the duke and duchess did not have an over-arching “philosophy” they followed but would be committed to a number of core themes in the years ahead.

William is now into the second year of his successful environmental Earthshot Prize and he met one of the inaugural winners during the final day of the tour in the Bahamas while Kate’s passion for the early years development of children was highlighted in a speech at a Jamaican school.

For many years they have both campaigned to raise awareness about mental health and in the Bahamas the couple talked with emergency service workers and nurses about the importance of looking after their wellbeing as they battled the pandemic.

William’s desire to do things his way will see a smaller household supporting the couple – they have just under 40 staff at the moment – when he becomes the Prince of Wales.

His father Charles has well over 100 people in his household but the heir to the throne carries out a greater number of engagements than his son and heads, or supports a significant number of organisations.

The couple carried out all their engagements in the Caribbean together but there are plans for the duchess, who recently visited Denmark by herself, to embark on more solo trips.

A source has reportedly said William believes the old adage associated with the royals of “never complain” is over and “He won’t be speaking out regularly but believes if the monarchy has something to say, then it should say it”.

Ending their trip to Belize, Jamaica and the Bahamas at the weekend, the future king acknowledged the monarchy’s days in those nations may be numbered as he stated the future “is for the people to decide upon”, and that he may not become head of the Commonwealth.

In a statement reflecting on the tour, William said who the Commonwealth chooses to be its leader “isn’t what is on my mind”, but what concerned him was its potential to “create a better future for the people who form it”.

He stressed that he and his wife Kate were “committed to service” and saw their role as supporting people, “not telling them what to do”.

William’s comment acknowledging Caribbean nations may seek to become republics recognised a process already in motion as during the tour Jamaica and Belize signalled this is a direction they maybe heading.

There has been some speculation the couple were ambushed by Jamaica’s prime minister when moments before they sat down to discussions, he suggested his country would look to become a republic.

William and Kate were described as looking uncomfortable at the time but a close aide said he was not aware of any atmosphere afterwards.

The couple received the support of Education Secretary Nadhim Zahawi, who said their tour had been subject to “Twitter outrage”.

During an appearance on LBC Radio, he disagreed with the suggestion there were “local difficulties” during the trip.

Commenting on the contentious image of the couple shaking hands with locals behind a wire mesh fence in Kingston, he said: “You had (England football player) Raheem Sterling shaking hands with the same kids that Prince William and Catherine shook hands with and one is headlined as a wonderful outreach programme and the other is headlined differently, so I don’t buy that.”