The leader of the Scottish Tory party has refused to rule out the possibility of a pact between Conservatives and the Scottish National party (SNP) at Westminster if David Cameron does not win enough votes to command a majority in parliament in the 2015 elections.

Ruth Davidson, speaking at a packed fringe meeting in Birmingham, conceded that after the general election a “quite likely scenario” was “a minority government or a coalition government [with] either the Labour party or the Tory party in the lead”.

When quizzed about the prospect about joining hands with Scottish nationalists after the bitter independence campaign, Davidson said “in terms of who we go into coalition with, were we to be the largest party … the numbers do the talking on this.

“Certainly my experience of the Scottish parliament is that the way bills are passed shows you which parties can form a government. I think we will see the same at Westminster.”

The four Scottish administrations since the devolved parliament was set up has seen two coalition governments between Labour and the Liberal Democrats and two run by the SNP.

At present the SNP have six seats at Westminster, but the surge in their support base has caused pollsters to readjust the party’s prospects for the general election.

Peter Kellner, of YouGov, said the SNP could make huge gains at Westminster, possibly reaching 26 seats – almost half of the 59 constituencies north of the border – at Labour’s expense. Kellner said Labour has “big problems” in Scotland after failing to convince many of their traditional supporters to vote against independence.

Writing on his blog, the pollster said: “A close Labour-Tory race would prevent the formation of either a majority Lib-Lab or Lib-Con coalition. Any prime minister would need to look elsewhere for extra support.

“Would Cameron need to buy off Ukip? Would Miliband need a deal with the SNP? In either case, would we have a three-party coalition or some other confidence-and-supply arrangement?”

Davidson warned about the SNP’s chances at Westminster, but added that she would seek to work with nationalists on the cross-party devolution commission under Lord Smith, which has been tasked with delivering more powers to the Scottish parliament.

“I read polls like everyone else and even the great Pete Kellner would say they are a snapshot of where we are at the time. I would be astonished if the SNP took anything like 20 seats off Labour at the next election,” she said.