Writing in The Telegraph, James Frayne, an electoral strategist at Public First, warned the Tories that this week’s migration figures would have an “immediate, direct impact on the polls”.
Mrs Braverman has been pushing to axe the visa and only allow graduates to stay for six months to find work, as the MAC originally proposed in 2018. Its advice was ignored.
She has also proposed a ban on one-year masters students bringing dependants. The policy is close to being agreed.
Prof Bell said it was “perfectly reasonable” for the Government to review this, but not for PhD students.
An internal note of a Whitehall meeting last October revealed her frustration when the figure for dependents was 80,000.
“She feels over 80,000 dependent visas is too many,” it said.
“She described the graduate visa as something that ‘says you can stay here for two years and you don’t have to work and you don’t have to study’.”
As well as clashing on graduate visas, Mrs Braverman is at odds with the Treasury over foreign workers.
The Home Secretary has argued for curbs on foreign labour by raising the minimum salary threshold for skilled workers, which is currently £26,200.
In a speech last week, she also said Britain should fill job vacancies with its own HGV drivers, butchers and fruit-pickers.
However, these measures are not expected to be adopted this week amid Treasury concerns they would exacerbate labour shortages.
The Treasury is understood to believe this would feed wage inflation, driving up prices in the wider economy.
A source said: “We’ve got to get rid of inflation, it’s corrosive.”
A minister in another Whitehall department shared the concern about the “inflationary effect”.
“My number one priority is finding people to do jobs,” said the minister.
However, Right-wing Tories criticised the Treasury amid a growing civil war within the party on immigration.
Miriam Cates, the MP for Penistone and Stocksbridge, said: “By allowing almost unlimited migration, there is no incentive for training up our own.”
A former minister said: “Migration at these numbers only leads into the Treasury orthodoxy of a low-wage, low-growth, low-skilled agenda.”