Every morning, Mohammed Al Muhandes wakes up in a hotel in Leeds, England, and wonders how to pass the day.

Along with dozens of other asylum seekers, he eats the same breakfast each morning, then returns to his room or walks in a nearby park. The 9.58 pounds, or $11.90, he is given each week is barely enough for one return bus trip to the city center (£4.50) and a cup of coffee. Asylum seekers in Britain are not allowed to work.

Mr. Al Muhandes, 53, who has a master’s degree in mechanical engineering, tries to stay busy, taking free classes and spending time in a local nature reserve, but he has waited almost five months for a decision on his case. While he is overwhelmingly grateful to have escaped conflict in his home country, Yemen, the uncertainty is hard.

“It’s like I am waiting for something, and I don’t know when it will come,” Mr. Al Muhandes said. “It’s like I am blind.”

For some, this limbo can last for years — a wait exacerbated by deep-rooted problems in Britain’s immigration system.

On Wednesday, the Conservative government’s flagship policy to send asylum seekers to Rwanda was left in disarray when the country’s highest court declared it unlawful. Even as Prime Minister Rishi Sunak pledged to find a way to override the court, critics said the policy was a distraction from the most pressing issue: an enormous backlog of unresolved asylum cases that has ballooned under the Conservatives, to 140,000 this year from about 22,000 in March 2018.

About 50,000 people are being accommodated in hotels leased by the government — at times as many as 350 — at a cost of £8 million a day. In total, the asylum system has cost taxpayers nearly £3.97 billion, or around $4.8 billion, in the past year — nearly double what it was the year before, according to official data.

Migration experts warn that costs will only rise the longer that fundamental flaws in the system remain unaddressed.

“The Rwanda policy, even if it was smoothly implemented, was only ever going to be a partial answer to the larger asylum question,” said Rhys Clyne, an expert on migration at the Institute for Government, a British think tank. “There are much wider questions the government needs to address.”

Britain is not alone in grappling with rising migration, driven by factors including conflict and climate change. But the Conservatives, who have held power for 13 years, have framed the debate around a rise in small boats crossing the English Channel. Mr. Sunak has repeatedly pledged to “stop the boats,” and his former home secretary, Suella Braverman, called them “an invasion.”

Arrivals by boat accounted for less than half of asylum claims last year. The rise in arrivals “is only a part of the story,” said Peter Walsh, a senior researcher at Oxford’s Migration Observatory. “I think probably the bigger part is that decision-making just hasn’t kept up with the applications.”

For one thing, caseworkers have been processing far fewer asylum claims than they used to. From 2015 to 2016, each caseworker made about 100 decisions a year. From 2021 to 2022, that fell to 24 decisions a year. Mr. Walsh said the drop reflected high staff turnover — which left inexperienced decision makers at the helm — low morale and policy changes.

Recently, the government hired more than 1,000 new caseworkers in an effort to tackle the backlog, and it heralded its success in cutting the so-called legacy backlog — defined as applications submitted before June 2022. That is when new, tougher migration laws came into force that said anyone arriving by “illegal” means would never have their asylum claims heard in Britain. Now, these new cases are piling up.

“The government now does have these larger numbers of asylum decision makers at its disposal,” Mr. Walsh said, “and if it does invest in additional streamlining and additional training, then it’s perfectly plausible that the backlog could begin to shrink.”

Amid criticism of the mounting costs, the government said last month that 50 hotels would stop taking asylum seekers. Robert Jenrick, Britain’s immigration minister, said that was possible because “our work to stop illegal migration is having a real impact — small boat crossings are down by more than 20 percent so far this year.”

Data obtained in a freedom of information request by the BBC suggested that would still leave hundreds of hotels in use. For months, the government has vowed to move people into former military barracks and onto barges, like the Bibby Stockholm, but the numbers living there are still small.

Meanwhile, each number in the total backlog — which reached 136,944 in August and includes people living in the community or with family — is a person waiting for an answer.

Leeds, where Mr. Al Muhandes lives, is in a northern region of Britain with one of the highest numbers of asylum seekers, according to the Refugee Council. He did not arrive by small boat, but on a flight that landed in London at Heathrow Airport in July.

“I lived in Yemen throughout the civil war in a hot spot,” he said, referring to the conflict that began in 2014. He worked for more than a decade in a senior government role, but while abroad for training, a friend warned him not to return because of threats against his life. He flew to Britain and immediately claimed asylum. He worries constantly about his wife and children, who are still in Yemen.

Ali, from Sudan, lives in the same hotel as Mr. Al Muhandes, and the two became friends. Both say the inability to work and the sense of isolation have been difficult.

After fleeing his home in Khartoum for Egypt with his wife and children when civil war erupted this past spring, Ali, 52, flew to Britain and claimed asylum, hoping to eventually be reunited there with his family.

“Sometimes at night I can’t sleep because, you know, my mind is on my country, my mind is on my family,” Ali said, asking to use only his first name over fears that speaking out could affect his case.

Residents in the hotel were recently told they would each receive a roommate in the coming weeks, one of the ways the government is cutting its use of hotels. Charities in Leeds, like the Refugee Education Training Advice Service, or RETAS, that provide practical support for asylum seekers say it has been difficult to keep up with policy shifts.

“A lot of things have changed — not for the better, to be honest,” said Yasir Mohamed, a volunteer service manager at RETAS. “It’s getting worse, and we see it.”

The majority of the staff and volunteers, including Mr. Mohamed, who came to Britain five years ago from Eritrea, have lived the experience of the system, having themselves received asylum in Britain. The charity offers education, employment support and other programs to support integration.

On a recent morning, asylum seekers from Iraq, Eritrea and Iran sat in a classroom in the RETAS office listening to Alison Suckley, their teacher.

“I live in Leeds,” Ms. Suckley said, slowly enunciating each word, and the class repeated her. As she took the pupils through a series of exercises to describe their likes and dislikes, one woman declared, “I love bread.” Those around her nodded in agreement, and the room erupted in laughter.