Paul and Claire McGinley are on a 99-day round-the-world trip on The Queen Mary 2 luxury cruise liner.
It was supposed to dock in Hong Kong but now the ship will spend longer in Singapore instead.
Mr McGinley, 52, of Wakefield, a former Leeds Council employee, said: "Although we are disappointed to be missing out on time in Hong Kong we appreciate Cunard's priority is the safety of everyone on board."
Speaking from the Strait of Hormuz near Iran, he said he and his wife, 49, a civil servant in Leeds, were grateful that Cunard had given plenty of notice.
He said: "People on board are being philosophical about the decision."
The change came after China and Hong Kong took steps over fears of the coronavirus spreading.
Britons returning from coronavirus-hit Wuhan in China will be put in quarantine for 14 days.
Officials are looking at taking passengers to a military base once they arrive home, the Department of Health said.
Downing Street said the Britons returning from Wuhan had agreed to be placed in "assisted isolation".
A source said: "We are expecting about 200 British nationals to be on board, there is capacity on the flight for everybody.
"On arrival passengers will be safely isolated for two weeks with all necessary medical attention."
Number 10 refused to confirm where the Britons would be taken following the civilian charter flight to airlift them from the region.
Mr Hancock tweeted: "We are working hard to get British nationals back from Wuhan. Public safety is the top priority.
"Anyone who returns from Wuhan will be safely isolated for 14 days, with all necessary medical attention."
The move comes after Britons returning to the UK expressed fury after being told they must "self-isolate" - while also making their own way home from the airport.
The Foreign Office updated its advice on Tuesday to warn against all but essential travel to mainland China, saying it may become more difficult for British nationals in other provinces to leave.
On Wednesday, British Airways announced it was suspending all flights to and from mainland China with immediate effect.
The death toll in China from coronavirus has risen to 132, with confirmed infections surging to nearly 6,000.