Trade minister Nigel Huddleston stressed that there would “always be peaks and troughs” in levels of immigration, with figures next week expected to show a surge in arrivals to the UK.
Some estimates suggest annual net migration, immigration minus emigration, could hit 700,000 or more, up from just over 500,000 in the year to June 2022, despite Brexiteers’ claims that quitting the EU would allow the Government to take back control of Britain’s borders.
In what appeared to be an attempt to pre-empt this rise in immigration, Mr Huddleston told Times Radio: “For certain periods of time, sometimes it goes up, sometimes it goes down.
“The key thing is having control ourselves and certainly in the long term we need immigration to come down because that is what has been causing some challenges in local areas for a long period of time.
“But every now and again we also need more people to come into the country.”
Mr Braverman was due to argue that there is “no good reason” the UK cannot train its own workforce of lorry drivers and fruit pickers, in a speech that will stress the need for overall immigration to the UK to come down.
The Home Secretary will be among the speakers at the National Conservatism Conference later on Monday, which comes only days after a similar gathering of Tory MPs and grassroots members in Bournemouth.
Her speech, which will be seen as a warning to Cabinet colleagues against relaxing immigration visa rules in a bid to boost growth, comes as Rishi Sunak grapples with signs of discontent and division with his party’s ranks.
Ms Braverman was set to say: “I voted and campaigned for Brexit because I wanted Britain to control migration. So that we all have a say on what works for our country.
“High-skilled workers support economic growth. Fact.
“But we need to get overall immigration numbers down. And we mustn’t forget how to do things for ourselves.
“There is no good reason why we can’t train up enough HGV drivers, butchers or fruit pickers. Brexit enables us to build a high-skilled, high wage economy that is less dependent on low-skilled foreign labour.
“That was our 2019 manifesto pledge and what we must deliver.”
But her stance appeared to be at odds with Mr Huddleston.
He stressed: “Many people are coming in just for temporary reasons, for example students, and that is often a good thing.
“But also we need temporary workers as well sometimes, hence the seasonal agricultural workers programme.
“I believe overall it would be good to have immigration come down,that is certainly the view of my constituents.
“However, there will always be peaks and troughs with this over individual periods of time.”
In a sign of tensions with the Conservative Party, Thatcherite former Cabinet minister Sir John Redwood said he would push for "big changes" in migration policy and refused to say whether Rishi Sunak should lead the party into the next election.
Asked whether he supported the Prime Minister on BBC Radio 4's Today programme on Monday, Wokingham MP Sir John said he was focused on "policy not on people".
He added: "The current focus is on policy and I am an optimist. I think this Government could do well. It could make changes for the better.
"I and my colleagues are desperate for it to do so.
"It needs to make big changes on its attitude towards Brexit, on its attitude towards economic growth and on migration."