Immigration is at the heart of voters' dissatisfaction. A majority of participants of a new poll said Boris Johnson's dealing of Channel crossings is not right.
Migration is the performance area in which Mr Johnson received the worst ratings, with only 21 percent approving.
Some 55 percent of the public and 77 percent of voters who backed the Conservative Party at the last election believe the Government’s strategy in managing Channel crossings is "too soft".
Home Secretary Priti Patel is under pressure for her role in combatting the migrant crisis, too. 53 percent of voters disapproved of her performance, while only 19 percent approved in the Sunday Telegraph poll.
In July, Ms Patel signed a ￡53million deal with the French government to increase patrols, boost aerial surveillance and enhance security infrastructure at ports.
However, the agreement has not proven successful yet.
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This month alone, arrivals have reached 5,000 – the highest monthly figure ever.
The numbers raise fears that, if migrants are risking their lives in the cold temperatures and dangerous conditions at sea, spring could...
So far this year, more than 24,500 migrants have reached the UK – nearly three times as many as last year.
Groups of children and adults were again pictured arriving in Kent yesterday.
A source told The Times: "Boris is exasperated.
"He sees this as one of his biggest priorities and he’s concerned that after two years there are still no viable solutions.
"He’s told ministers to redouble efforts to fix this, no matter how difficult it is.
"If it looks bad now, it’s going to look much worse in spring when it’s warmer."
Mr Johnson was challenged over his handling of the Channel crossings by MPs at a meeting of the 1922 committee on Thursday night.
Sir Iain Duncan Smith said: "Migration was in our manifesto, it was in our DNA.
"If we don't do it, they won't forgive us."
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Dozens of MPs showed they agreed as they banged their hands on the desks and walls of the committee room, and other MPS — at least three — reportedly expressed similar concerns.
The Prime Minister was warned stopping the flow of illegal migration across the Channel would require more than the forthcoming Nationality and Borders Bill.
It was on Friday announced that Cabinet Office minister Stephen Barclay is to review how to prevent migrants from crossing the Channel.
Mr Barclay will be in charge of exploring what ministerial departments can do to push the issue up in the Government's and civil service's list of priorities.
The online survey, by Redfield & Wilton Strategies, showed housing as another area in which voters believe the Tories are underperforming, with less than a quarter of voters approving of the Government's approach.
Despite pledging ￡58million to councils across England as part of Mr Johnson's "levelling up" agenda, experts argue the measure is not enough to help the thousands of Britons who are priced out of the property market.
Ross Counsell, chartered surveyor and director at GoodMove, told Express.co.uk when the plans were announced last month: "We have seen a prevailing idea among politicians that building more houses is a solution to the current housing crisis.
"However, building these houses without being aware of who can afford to purchase them, does little to help those with lower incomes to get onto the property market."