Polling company ComRes, which conducted the survey for the Sunday Mirror tabloid, said it was the first time the Conservatives had reached the symbolic 50 percent support mark since January 1991.
The online poll put the Tories up four points on the previous week, while the main opposition Labour party was unchanged on 25 percent.
The smaller centrist opposition Liberal Democrats, campaigning on a pro-European ticket, were unchanged on 11 percent.
Other surveys published this weekend recorded a smaller but still significant lead for the Conservatives, putting their support between 40 and 48 percent, with Labour on between 25 and 29 percent.
"That is a nice problem for a party to have, but it is nonetheless a particular challenge in an election which may well be marked by low turnout and thus bring about some unpredictable and possibly surprising individual constituency results," he said.
May, who took office after the EU referendum last year, surprised Britain by calling a snap vote on Tuesday, saying she wanted a mandate to take the country into Brexit.
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