The British government would expect passport checks between Scotland and England if a looser immigration policy were adopted north of the border after independence, according to the home secretary, Theresa May.

Her view is at odds with the Scottish government's aim of keeping passport-free travel.

Risking attacks for misrepresenting Scottish government policy and her own department's stance on border policy, she claimed that the SNP administration's pledge to pursue "healthy population growth", outlined in the white paper on independence, will "undermine" Tory policies south of the border.

"If the people of Scotland vote to leave the UK there would be profound changes for migration policy," she said in a speech at the Scottish Conservative Party conference in Edinburgh on Friday.

"An international border would be created where one does not currently exist. This would have implications for people travelling to visit family, go on holiday or do business, and for our economies more generally.

"Buried deep in Alex Salmond's white paper is the admission that, just like the last Labour government, a separate Scotland would pursue a looser immigration policy.

"That would undermine the work we have done since 2010, and the continuing UK could not allow Scotland to become a convenient landing point for migration into the United Kingdom.

"So that would mean border controls between a separate Scotland and the United Kingdom," she said. "Passport checks to visit friends and relatives. A literal and figurative barrier between our nations."

The Scottish government's independence white paper said that Scotland should join the Common Travel Area between the UK and Ireland, which allows free movement between both countries and will soon include a universal visa for both countries.

In January, Alistair Carmichael, the Scotland secretary, had agreed it would make sense for Scotland to join the Common Travel Area provided it dropped plans to have more liberal, open immigration rules than the UK.

Implying that border controls would mean a return to the "bitter days" of the border disputes of hundreds of years ago, May also claimed that "we already know that a yes vote would mean that, when it became separate, Scotland would no longer be part of the European Union."

She said European Commission president José Manuel Barroso "has been quite clear about that", referring to Barroso's claim last month it would be impossible for an independent Scotland to smoothly join the EU while it negotiated independence from the UK.

May added that after Scotland "went cap-in-hand to beg for admission" to the EU, it would be forced to join the Schengen treaty on open borders – a treaty that would mean border controls with the UK.

Last month, David Cameron told journalists in Scotland that the UK would actually support Scotland's application to join the EU, implying it would smooth the way for a quick accession.

Earlier in the day, Cameron pledged that the Tories would back plans to give Scotland more tax and law-making powers, stepping up the battle to win over undecided voters before September's independence referendum.