The duty-free shop on Deck 7 of the Isabelle has been turned into a storage locker and pantry, with suitcases heaped in the perfume section and refrigerated display cases crammed with labeled grocery bags. The ship’s shuttered casino has become the go-to hangout for teenagers. And the Starlight Palace nightclub on Deck 8 is where women meet to make camouflage nets for Ukrainian soldiers back home.

“It makes me feel closer to them,” Diana Kotsenko said as she tied green, brown and maroon cloth strips onto a net strung across a metal frame, her 2-year old, Emiliia, tugging at her knees.

For the past three months, Ms. Kotsenko and her daughter have been living on the Isabelle, a 561-foot cruise ship leased by the Estonian government to temporarily house some of the more than 48,000 refugees who have arrived in this small Baltic nation since the Russians invaded Ukraine in February.

The ship, which once ferried overnight passengers between Stockholm and Riga, Latvia, is now berthed next to Terminal A in the port city of Tallinn, Estonia’s capital. Its 664 cabins house roughly 1,900 people — most of them women and children who come and go as they please through the ship’s cavernous cargo door.

The residents are a tiny fraction of the more than 6.3 million Ukrainians who have streamed into Europe. Their lot is a sign of the strains that the flood of refugees is having on countries that have mostly welcomed them.

Isabelle was leased from an Estonian shipping company, Tallink, in April for four months as an emergency shelter. But with nowhere else to put its residents, the government has extended the contract through October.

The shortage of homes for refugees is creating intense pressure across the continent and Britain. Low-cost housing is scarce, and rents are rising.

In Scotland, the government announced last month that it was pausing its program to sponsor Ukrainian refugees because of the lack of accommodations. In the Netherlands, scores of refugees have been sleeping on the grass outside an overcrowded asylum center in the village of Ter Apel. On Monday, the Dutch Council for Refugees announced plans to sue the government over shelter conditions that it said fell below the minimum legal standard.

Of all the challenges facing Ukrainians who escaped to safe havens, the most pressing is access to housing, according to a new report from the Organization for Economic Development and Cooperation. The problem of finding longer-term accommodation is expected to only worsen given rising inflation, the report concluded.

“Early evidence also suggests that a lack of housing is a primary motivation for refugees to return to Ukraine, in spite of safety risks,” it said.

Governments — which were already struggling to house refugees and asylum seekers from other parts of the world — have set up emergency intake facilities, rented hotels and provided financial support to host households. But with reception centers overflowing, countries have been forced to scramble for other solutions. Schools, hostels, sports stadiums, cargo containers, tents and even cruise ships have become stopgap accommodations.

In Estonia, the government enlisted Tallink, which had leased out its ships in the past as temporary housing for construction projects, military personnel and events. One housed police officers during a Group of 7 meeting in Britain last year. Another was chartered during the global climate conference in Glasgow last fall.

The Scottish government turned to Tallink when it faced its own refugee housing crisis, and last week, the first group of Ukrainians moved into a Tallink ship docked in Edinburgh’s port.

The Netherlands, too, is using cruise ships. In April, 1,500 refugees moved into a Holland America Line vessel docked in Rotterdam. Last week, the government’s asylum agency announced that it planned to charter two additional vessels from Tallink for seven months.

The floating solutions have been greeted with skepticism or even hostility in some quarters. Before the Tallink ship arrived in Scotland, some news accounts breathlessly warned of the risks of a Covid-19 outbreak.

The Dutch government came under scorching criticism for a now-abandoned proposal to put refugees on a ship anchored off the coast in open water, making it difficult for people to come ashore.

In Tallinn, the Isabelle had been out of service because of travel restrictions since the pandemic began in 2020 before it was put to use for the refugees. Natalie Shevchenko has lived on it since April. She has searched for an apartment in town but hasn’t been able to find one she can afford.

A psychologist from Kyiv, Ms. Shevchenko has been working with mothers and children onboard, helping them adjust.

“When you live on a ship, it’s like a big community,” she said.

On a recent evening, a steady flow of people entered or left the ship after a brief pause at the security desk to scan their identification cards. On Deck 8, diners lingered over coffee in the Grand Buffet. “The food is good,” Ms. Shevchenko said. “There’s a lot of desserts, cakes and ice cream.”

In a lounge area, a dozen people sat in front of a television set watching the news from Ukraine. Cliques of chattering teenagers roamed the long decks or sprawled on chairs near the casino’s empty blackjack tables. Two floors below, near the staircase where strollers were parked, children spread out on the blue and white carpet to play games, while two giggling boys slid down a short brass banister under the watchful eyes of mothers.

Volunteers have donated toys, clothes and baby carriages, and have organized activities and excursions. On Deck 10, refugees can meet with social service workers. Bulletin boards around the ship were filled with announcements in Ukrainian about summer camp, free exhibitions, and language and culture courses. The newly named Freedom School is scheduled to start classes in Ukrainian and Estonian in the fall. Players from an Estonian soccer club came on board last weekend to lead a practice clinic.

When Ms. Shevchenko needs solitude, she escapes to one of the lower car decks. She shares a claustrophobic sixth-floor cabin and bathroom with another woman she did not previously know. The space between the beds is narrower than an airplane aisle. Bags, shoes and boxes are stuffed under the beds. A white rope crisscrosses the walls to hang laundry.

“Here’s our kitchen,” Ms. Shevchenko said, pointing with a laugh to a shelf with bottles of water and soda. A flowerpot, a gift for her recent 34th birthday from the Estonian psychologists she works with, sits on the windowsill.

“We’re lucky to have a window,” she said. Some cabins on lower decks don’t have one. It’s a problem for people who had to shelter underground in Ukraine, she said: “Some people have panic attacks.”

A few doors down is the cabin that Olga Vasilieva and her 6-year-old son share with another mother and son. The two women use the unfolded upper bunk beds to store toys, bags and snacks, and sleep with their children in the narrow beds below. Bigger cabins are reserved for families with three or more children.

One of the benefits of living with so many other families is that there are lots of children to play with. “He has so many friends,” Ms. Vasilieva said, turning to Ms. Shevchenko to translate.

Ms. Vasilieva wants to return home before the school year starts, but so far, it hasn’t been safe. Although she had two jobs in Ukraine, Ms. Vasilieva said, she doesn’t work now because she has no one to care for her son. She said she received roughly 400 euros a month from the Estonian government. About a hundred of the refugees work for Tallink, in kitchen and housekeeping positions. Others have found jobs in town.

Inna Aristova, 54, and her husband, Hryhorii Akinzhely, 64, who arrived in May after a hard trek from Melitopol, work in a laundry sorting sheets and towels. They haven’t been able to find an affordable apartment.

“I feel like a guest in this country,” Ms. Aristova said, “not home.”

Tears filled her eyes. Her most acute anxieties center on her 21-year-old son, who is in the army. She doesn’t know where he is, a security precaution, but they try to text or speak as often as possible.

“He is so young,” she said. “Every day I am thinking about him.” Ms. Shevchenko, who was translating, bent down to hug her.

In the Starlight Palace, Ms. Kotsenko and a handful of mothers and teenagers worked on the camouflage nets, cutting strips of cloth and attaching them. When finished, the cover will be sent to the Kherson region in southeastern Ukraine to hide tanks from Russian bombers.

Ms. Kotsenko also doesn’t know where her husband is stationed in Ukraine. She and her daughter escaped from the embattled city of Mykolaiv.

Another woman from the same city pulled out her phone to show Mykolaiv on a map. An animated red burst marked the spot, indicating heavy fighting.

She had just received a long text from her neighbor with a series of photos showing bloody corpses of people and dogs lying on the streets, killed by Russian shells that morning.

Some of the women Ms. Shevchenko has counseled have told her that they have decided to return to Ukraine. But, she said, what “you dream about your home” may not match the reality.