The local British elections, long scheduled for May 4, were expected to be a bellwether of opinion looking ahead to a general election in 2020. But now that Prime Minister Theresa May has called an election for June 8, the May results are of greater import — and the one with the greatest import, for Britain and perhaps beyond, was the mayoral election for the new West Midlands constituency.

About one-third of its population is in the city of Birmingham, with its large Muslim population but also some comfortable upper middle class precincts. To the east, with about one-fifth of the population, is the factory town of Coventry and its bombed out (in World War II) cathedral and the intervening suburb of Solihull.

To the west, with a bit more than 40 percent of the West Midlands population, are the industrial hubs of Walsall, Wolverhampton and Dudley, with intervening towns.

I've spent some time in the West Midlands, with Gisela Stuart, the New Labour MP, watching her hold onto her leafy Edgbaston seat (once Neville Chamberlain's constituency) in 2015, and with Khalid Mahmood, a Muslim Labour MP, watching him face down radicals. I've driven around the suburban landscapes with their enclosed malls and WiFi-handy McDonald's, cul-de-sac subdivisions and banks of soot-encrusted rowhouses.

The big result from West Midlands is the election of Conservative candidate Andy Street as mayor over Labour candidate Sîon Simon. Both have interesting backgrounds: Street was CEO of John Lewis, probably Britain's largest department store, for more than a decade; Simon was a Labour MP from Birmingham and an MEP (member of the European Parliament) from a wider regional constituency.

On first-choice votes, Street led Simon by 42 to 41 percent; under the new British system, voters could indicate a second-choice candidate, with votes from those who had picked third- or lower-finishing candidates distributed to one of the two top finishers. Simon had more second-choice votes from the 17 percent of those favoring other candidates, but not enough to close the gap, and Street was declared the winner by a 50.4 to 49.6 percent margin.

This is a big win for Conservatives, and in a constituency where no one a few years ago would have expected them to be competitive. The Labour party won 21 of the 28 House of Commons seats in the West Midlands in the May 2015 general election . Labour candidates, by my calculation, won 42 percent of the popular votes and Conservative candidates 33 percent. But in the Brexit referendum, the West Midlands voted 59 to 41 percent to Leave the European Union; even the central city of Birmingham, expected to vote remain (as 60 percent of London did) voted 50.4 percent for Brexit. Turnout in this referendum was higher (1,301,711) than in the general election 13 months before (1,163,175).

Turnout was much lower in the West Midlands mayor election (515,930). The opposition to Brexit of almost all leading Labour party figures (Gisela Stuart was an unusual exception) may have loosened the party's hold on many traditional working class Labour voters, and certainly the extreme left-wing and politically tone deaf politics of the current Labour leader Jeremy Corbyn has turned some of them off.

But the big story is perhaps the increasing acceptability of the Conservative party — a party at least somewhat transformed from its previous image. Brexit helped: only 33 percent in West Midlands voted for Conservative MPs, but 59 percent voted for Brexit.

And David Cameron, with his posh schooling and his strategy of appealing to cosmopolitan voters by supporting same-sex marriage and environmental causes, may have had less appeal than Theresa May, with her more modest provincial background and determination, right after the referendum in which she quietly supported Remain, that "Brexit means Brexit."

In addition, Andy Street in his campaign emphasized his long involvement in Birmingham civic activities and non-involvement in the national Conservative party. That helped him win 42 percent of first-choice votes and 50.4 percent when all second-choice votes were allocated — showings very far ahead of the 33 percent for Conservatives in the 2015 general election.

Polling for the general election suggests this trend is not peculiar to the West Midlands. Current polling shows Conservatives leading Labour by 48 to 27 percent. That's a decline for Labour from the 31 percent it won in May 2015, but it's dwarfed by the increased support for Conservatives, up from 37 percent to an average of 48 percent.

This represents a sharp decline for the United Kingdom Independence Party from its 13 percent in May 2015 to 7 percent now, with virtually all the difference going to the Conservative line. When Conservatives were divided on the desirability of the European Union, voting Ukip arguably was a way to pressure them to take a anti-EU stand. Now that Britain has voted to leave the EU, and its Conservative prime minister has made it absolutely clear she will honor the voters' decision, what point is there in voting Ukip any more?

There are interesting lessons here, ones with implications beyond Britain.