Neil and Victoria Hanlon, from Bridgwater, are onboard the Grand Princess around 20 miles off the coast of California, alongside 140 other UK nationals.
The couple previously likened quarantine to 'being in a prison', but added they understood why it was happening.
The cruise operator said groups of guests and crew are being tested for Covid-19, after a passenger on an earlier voyage died and at least one other became infected.
Twenty-one people on board a huge cruise ship off the California coast have tested positive for the coronavirus including 19 crew members, US Vice President Mike Pence said last week.
Speaking to ITV News, Neil said he had seen a few people on the ship who "did look quite ill".
We passed a few people on the ship, probably about a week or so ago that did look seriously ill, very ill, they had masks and stuff on. We were in the lift with them, which probably wasn't a good thing, but they were going down to level four which is where the medical centre was. We asked them if they were ok, their breathing was horrendous, they said they had bronchitis - whether that was the truth I don't know, but he did look really ill.
In an announcement the captain told those on board that those infected would continue to be quarantined onboard until they could be taken ashore "and transported to local hospitals for ongoing care".
He added that this was an "evolving situation".
Speaking to ITV News West Country after the announcement, Neil said he and his partner felt like they had been "abandoned" by the UK government.
Our government, what a let down. We've heard nothing whatsoever. Our foreign office has not told us anything and has not been in contact. Basically, we feel very, very abandoned.
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In response, the UK government said it was working "intensively" to repatriate Britons on board the vessel - including Neil and Victoria.
A Foreign Office spokesman said on Sunday (March 8): “We are working intensively with the US authorities on arrangements for a flight for British nationals who are currently on the Grand Princess Cruise ship off the coast of California.
“We remain in close contact with the local authorities and will work with them on their plans.
“We are also in contact with the Grand Princess’ staff, and are ready to support any British nationals who need our assistance.”
Despite the quarantine however, the couple added that spirits were high - with many chatting amongst themselves on a Whatsapp group.
[We're] trying to make lighthearted jokes really, we're trying to keep our spirits up - it's early days! It's four walls, and you're not allowed out when your food is at the door you've got to be a distance away, they've got masks on, it is what it is. It's not a nice feeling, but they're doing what they've got to do.