However, Professor Thrasher said his projection was some way short of the win being forecast by opinion polls.
All 88 councils in England, Wales and Scotland have declared their final results and at latest count the Conservatives have a net gain of 558 councillors, Labour are down 320 and the Lib Dems down 37. Results from the local elections suggest the message is getting through.
Labour were down 150 seats and lost control of one council.
In a highly symbolic victory, Conservative Ben Houchen became the first elected mayor of Tees Valley, in Labour's north-eastern heartland, beating Labour's Sue Jeffrey by more than 2,000 votes in the second round of counting.
Conservatives won the West of England metro mayor contest and topped the first round of voting in the West Midlands, while Labour claimed the mayoralties in Greater Manchester, Liverpool, Doncaster and North Tyneside.
It also lost Welsh councils Blaenau Gwent and Merthyr Tydfil to independents, as well as Bridgend.
Meanwhile, Jeremy Corbyn said Labour had "had some hard results overnight".
"It looks as if we have made so far some encouraging gains? but it?s very early days yet".
UKIP lost nearly all council seats the party had previously held.
Ukip's vote was "bleeding off to the Conservatives", Mr Kaufmann said - an analysis shared by party leader Paul Nuttall.More news: Hong Kong | Gov't rejects asylum for refugees who sheltered Snowden
"Slowly but surely English is losing importance in Europe", Juncker told a conference in Florence before switching into French and drawing applause from his audience of European Union officials, local leaders and Italian students.
Al Jazeera's Barnaby Phillips, reporting from Westminster, said it was striking that the Conservatives had made gains in Scotland, pushing Labour - once the dominant political force in Scotland - into third place, behind the Scottish National Party and the Conservatives.
The British general election is scheduled for June 8. When I said we could do this - people simply didn't believe me.
The Tories were up on 276 seats, up 164.
The Conservatives made sweeping advances across the United Kingdom, gaining more than 500 councillors.
He specifically warned of a Tory lurch to the Right if May was returned with a Tory majority up from 17 to a much bigger figure.
Ms Sturgeon said: "What we've seen across Scotland today of course is the SNP vote holding firm".
A BBC projection of the overall national vote share put Conservatives on 38% (up 13 points since 2013), Labour 27% (down two), Liberal Democrats 18% (up four) and Ukip 5% (down 18). Nationalist party Plaid Cymru gained 33 seats for a total of 202 with control of one council.
Labour lost over 100 seats and three councils, but retained control in the key cities of Cardiff and Swansea.