However, Professor Thrasher said his projection was some way short of the win being forecast by opinion polls.
The Conservatives have made sweeping gains in local elections, as Labour lost hundreds of seats, the Liberal Democrats' recovery stalled and Ukip was all but wiped out.
Conservatives also achieved shock victories in elections for regional mayors in the West Midlands and Teesside, as well as in the West of England.
Labour suffered a painful defeat in Glasgow, where it lost sway over the city council, under its control since 1980.
There was some good news for Corbyn, however, with former cabinet minister Andy Burnham elected Mayor of Greater Manchester, beating his Tory rival by more than 230,000 votes.
Despite a touted resurgence from the Lib Dems, Tim Farron's party failed to make any real gains and lost more than 40 seats.
Defending Mr Corbyn's leadership, he said he was a "honest, decent and principled" man but acknowledged that Labour needed to do more to communicate his strengths and its policies which he said were popular with the public.
As Ukip shed 109 councillors while holding a solitary seat in Lancashire, leader Paul Nuttall said the party was "a victim of its own success" over Brexit.
The Liberal Democrats had a mixed election, failing to break through against the Tories in the south-west England battleground.
The Conservatives made sweeping advances across the United Kingdom, gaining more than 500 councillors, winning tightly-fought battles for elected mayors in the West Midlands and Tees Valley and forcing Labour into third place in its former stronghold of Scotland.
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But he said: "He has been elected by almost half a million people twice in the last two years".
The Tories were up on 276 seats, up 164.
Ballots were counted Friday from contests for local councils in Scotland, Wales and many parts of England, as well as from mayoral competitions in several cities.
Labour emerged seriously diminished, losing five councils and with 133 fewer councillors.
And in Scotland the Rubbish Party - focused on anti-littering - won a seat.
"With the last two years spent on the development of polling methods specifically devised with the intention of confronting the Labour problem, the question must be considered that we've gone too far the other way", he said.
The SNP won 39 out of 85 seats, just four short of an outright majority, as Labour went from 41 to 31.
Ms Davidson said the results showed "only the Scottish Conservatives have the strength to fight back against the SNP".
"I wasn't sure if people could bring themselves to vote Conservative because we still have a mining heritage".
At the time of writing, the Tories had gained an extra 560 councillors.
Severe blows for Labour in the south Wales valleys, with independents taking control of Blaenau Gwent and Merthyr Tydfil.