A split at the top of the Conservatives on immigration policy has emerged after the Scottish Tory leader, Ruth Davidson, called on the government to consider scrapping its target of reducing the number of new arrivals to tens of thousands a year.

Davidson, who is on the liberal wing of the party, has previously defended the “tens of thousands” target pledged by David Cameron before the 2010 election, which has never been hit.

But writing in the Telegraph, she said: “By 2010, pollsters reported that immigration was consistently a top concern to voters. Since then, of course, the British government has failed to hit its self-imposed ‘tens of thousands’ target in any year.

“Brexit is a big reset button and should – in theory – make that much easier to do so. But we have to ask whether the target continues to be the right one.”

Davidson also called for No 10 to think about taking students out of the official immigration statistics.

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“If people don’t think that students should be included in the net migration numbers, let’s take them out and have a clearer picture of where we are. Currently, students can secure a post-study work visa if they secure a graduate-level job within three months of graduating. Should that timescale be extended?”

She called for a rational discussion on immigration instead of “easy slogans”.

No 10 declined to comment on Davidson’s views, but a senior government source said her suggestions “weren’t going to happen”.

Her remarks indicate a clear split with the Conservative government’s policy as Theresa May has stuck by both the target and the inclusion of students in the numbers, despite the reservations of some of her senior colleagues. Amber Rudd, the home secretary, is known to be much more open to changing policy on those issues.

The intervention is a sign of the Scottish Conservative leader flexing her muscles after she led 13 Tory MPs to victory north of the border at the election, allowing May to run a minority government based on her deal with the DUP.

Although Davidson is not an MP, the success of the Scottish Tories and her role as opposition leader in Scotland has given her a growing influence and she is often tipped as a potential future leader.

A survey published on Tuesday by the ConservativeHome website revealed Davidson was more popular with grassroots members than any cabinet minister, with a net satisfaction score of 81%.