But negativity has increased by eight percentage points from 29 per cent last year, the research by Ipsos and think tank British Future indicated.
The survey of 3,000 adults online in July and August showed 48 per cent of respondents support reducing immigration – an increase from 42 per cent last year.
Two thirds (66 per cent) of those questioned across England, Scotland and Wales said they were dissatisfied with the way politicians were dealing with the issue.
The level is the highest it has been since 2015 when the survey began, with the latest figure up from a low of 41 per cent in 2020.
The dissatisfaction is on both sides of the political divide but for different reasons, the research found.
100,000 migrants cross the Channel in five years - in pictures
Among Conservative supporters, 56 per cent were dissatisfied while slightly more than a fifth (22 per cent) said they were satisfied with the government’s handling of the issue. Among Labour supporters almost three quarters (73 per cent) were dissatisfied, with 8 per cent satisfied.
For 82 per cent of dissatisfied Conservative supporters, “not doing enough to stop Channel migrant crossings” was cited as their main reason why.
Last week, Labour accused the Prime Minister of having “failed to get a grip” on the issue as the milestone of 20,000 crossings this year was reached.
But Rishi Sunak continued to defend his “stop the boats” plan and insisted the government was making progress.
Among dissatisfied Labour supporters surveyed, fewer people (46 per cent) cited stopping Channel crossings as the main reason, while a similar proportion felt the current political approach was “creating a negative or fearful environment for migrants who live in Britain”, and the government was “not treating asylum seekers well”.
Only 4 per cent of dissatisfied Tory supporters chose “not treating asylum seekers well” as a reason.
More than two thirds of Conservative supporters (67 per cent) now favour reducing migration, while 38 per cent of Labour supporters favour reductions.
More than half (56 per cent) of Labour supporters said immigration numbers should either rise or stay the same.
“The government’s approach to immigration, particularly asylum and small boats, is disappointing everyone – but for different reasons," said Sunder Katwala, director of British Future.
“Liberals think it is inhumane, while hardliners think it isn’t achieving what has been promised. What they all have in common is the feeling that the government isn’t doing a good job.
“Attitudes to immigration are nuanced but the sharp divide along party political lines means we should expect a noisier, more heated immigration debate as Britain heads towards a general election.
“But politicians won’t rebuild public trust by raising the volume of the debate – that will take workable solutions, particularly on asylum, that balance control and compassion.”
Gideon Skinner, head of political research at Ipsos, said: “There is no simple answer to meeting voters’ demands on this issue, as views are split and often nuanced.
“For example, Britons also continue to support migration for specific sectors of work [especially health and social care], while control over who comes in is often as if not more important as the total numbers.
“But with an election on the horizon and attention on the issue of immigration and asylum unlikely to go away, there isn’t much trust in either of the main parties to get the balance right.”