Sir Keir Starmer faces mounting pressure over the small boats crisis after protests outside asylum hotels continued over the bank holiday weekend.
A poll suggested that voters believe the prime minister is failing to grip the problem, despite his government setting out measures to speed up removals.
It comes as Green Party co-leader Carla Denyer warned that "the far right feels emboldened and validated" by other political parties.
So far this year a record 28,076 people have made the perilous journey across the English Channel in small boats, 46% more than in the same period in 2024.
Like many other European countries, immigration has increasingly become a flashpoint in recent years as the UK deals with an influx of people fleeing war-torn and poorer countries seeking a better life.
Official figures released earlier this month showed a total of 111,084 people applied for asylum in the UK in the year to June 2025, the highest number for any 12-month period since current records began in 2001.
There were 32,059 asylum seekers in UK hotels by the end of the same month.
Protests and counterprotests at sites housing asylum seekers continued over the weekend and the government is braced for further legal fights over the use of hotels.
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A YouGov poll for The Times found that 71% per cent of voters believe Sir Keir is handling the asylum hotel issue badly, including 56% of Labour supporters.
The survey of 2,153 people carried out on August 20-21 found 37% of voters viewed immigration and asylum as the most important issue facing the country, ahead of 25% who said the economy and 7% who said the health service.
Ms Denyer, who is MP for Bristol Central, condemned threats of violence in the charged atmosphere around immigration.
"The far right feels emboldened and validated by other political parties dancing to their tune.
"The abuse I've been sent has got noticeably worse in the last few months, escalating in some cases to violent threats, which are reported to the police.
"It doesn't matter how much you disagree with someone, threats of violence are never, ever OK. And they won't silence me."
(c) Sky News 2025: Starmer facing mounting pressure over immigration as MP says far right 'emboldened'