EDINBURGH, May 19 (Reuters) - The leader of Prime Minister Theresa May's Conservatives in Scotland on Friday made a plea to supporters of Britain's opposition Labour Party to lend her their vote at next month's election to halt the march of the Scottish nationalists. Scots rejected independence in 2014, but the Scottish National Party (SNP) says they should have a fresh choice as they voted to stay in the European Union last year, at odds with the United Kingdom's overall decision to leave. The SNP has dominated politics north of the border for the last decade and won 56 of parliament's 59 Scottish seats at the last national election in 2015, following a collapse in support for Labour in one of its former heartlands. While the SNP is expected to take the majority again at a June 8 election, polls show Prime Minister Theresa May's Conservatives, who oppose another referendum, are on the rise. "Today, I want to speak directly to Labour party voters across Scotland ... The truth is, your party has left you, not the other way around," said Ruth Davidson, speaking alongside May at the launch of the Conservatives' Scottish manifesto. "It may well find its way back. But you know, and I know, it won't be at this election. So let me do a job for you. In great swathes of the country, it is only the Scottish Conservatives who are strong enough to take on the SNP. And in many places we can only win, if you join with us." A YouGov poll published on Friday put the SNP on 42 percent of the vote. The Conservatives, who have just one seat in Scotland, were second on 29 percent, with Labour on 19 percent. YouGov put support for independence on 45 percent, with 55 percent saying Scotland should remain in the United Kingdom, suggesting no change in opinion at all since the vote in 2014. May has said a second Scottish independence referendum cannot take place until the Brexit process has played out and only then if there is public consent for it. Even modest gains for the Conservatives could allow May to argue that the SNP's secession ambitions are misplaced. Asked whether the SNP winning a majority of seats in Scotland would be enough of a sign there is public consent, May said now was not the time to be talking about another independence vote.