The Duke and Duchess of Sussex, who begin their new life as non-working royals this week, have said they intend to spend the next few months concentrating on their family and privately supporting their charities.

The couple, who have relocated to California, will cease to be working royals and can no longer officially represent the Queen from Wednesday, as they seek to become financially independent.

Under their agreement with the monarch they will no longer post on Instagram under the @sussexroyal handle, which has 11.3 million followers, or update their SussexRoyal.com website. The Instagram account and website will remain online for the foreseeable future but will be inactive.

The couple are winding down their Sussex Royal Foundation, which was in the process of being established in the UK, and working on creating a non-profit organisation.

A spokesperson said: “The Duke and Duchess of Sussex will spend the next few months on their family and continuing to do what they can safely and privately, to support and work with their pre-existing charitable commitments while developing their future non-profit organisation.”

In a message on Instagram, the couple thanked their “community” of followers. “What’s most important right now is the health and wellbeing across the globe and finding solutions for the many issues that have presented themselves as a result of this pandemic.” They were “focusing this new chapter to understand how we can best contribute”. They added: “While you may not see us here, the work continues.”

Although there is no mention of where they are living, reports that Harry and Meghan had relocated to California appeared to be confirmed after the US president, Donald Trump, tweeted that they must pay for their own security. The couple’s spokesperson immediately stressed they “have no plans to ask the US government for security resources”, seen as confirmation the two had left Canada just ahead of the border closure with the US for all but essential travel.

Questions over their security remain. While the couple are said to have made “privately funded security arrangements”, no details are forthcoming on whether the Metropolitan police will still be providing protection for the couple, and their baby son, Archie. All three are understood to be in Los Angeles, where Meghan grew up, and where her mother, Doria Ragland, resides.

Harry’s sustainable travel initiative, Travalyst, will be established as an independent non-profit organisation. As the travel industry faces the global threat of coronavirus, Harry is said to be “working closely with each of the Travalyst partners to better understand how this non-profit organisation can aid in global recovery, especially by supporting communities, wildlife and the environment at the same time”.

The couple remain committed to their roles as patrons. There would be no additional information on their next steps made public for now, their office said. Frogmore Cottage will continue to be the Sussexes’ family home in the UK. As was announced in January, they will repay the £2.4m sovereign grant expenditure on the refurbishment of their home, pay rent and meet the running costs of the property.

They have recruited Catherine St-Laurent, who was the director at Pivotal Ventures, Melinda Gates’s women and families foundation, to lead their new charity. Their PR is being handled mainly by the firm Sunshine Sachs in Hollywood, as their 15-strong team at Buckingham Palace is dismantled.

Royal experts said the couple faced unforeseen challenges in establishing their new roles. “They must be reassessing the situation on a daily basis, given all the changes. Clearly the situation they are in is very far from that they anticipated when they first made public their proposals back in January,” said Joe Little, the managing editor of Majesty Magazine.

The royal author Penny Junor said the couple were in danger of becoming “pretty irrelevant” as the world battled Covid-19. “I think for the time being Harry and Meghan will probably become a distant memory.”

The royal family definitely had a role to play in a crisis like this, she said, but Harry and Meghan’s decision was “absolutely pushed to the back of the list of priorities”.

The couple are understood to have left their rented mansion on Vancouver Island last week, with unconfirmed reports that the border closure between the US and Canada hastened their decision. “It probably has happened more quickly than they originally planned. You have to feel sorry for them in many ways, because the timing of all this is totally wrong for all the things they hoped to achieve,” said Little.

“We have to look at them very differently now. What they do next is going to be very different from what the House of Windsor has been doing.”