British PM, David Cameron
Polls have closed in the Corby by-election - seen as a crucial mid-term test of David Cameron's premiership.
If Labour wins, it will be the first time in 15 years the party has taken a Tory seat at a by-election.
In other by-elections, Labour held both Manchester Central and Cardiff South and Penarth, in what has been dubbed "Super Thursday".
And millions have been voting in the first police and crime commissioner (PCC) elections in England and Wales, reports the BBC.
Voters in Bristol have also been to the polls to choose the city's first directly-elected mayor.
In Manchester Central, Labour candidate Lucy Powell (11,507) won with a majority of 9,936. Liberal Democrat Marc Ramsbottom (1,571) was second and Conservative Matthew Sephton (754) came in third.
The turnout of 18.16% is believed to be the lowest in a UK parliamentary by-election since World War II.
In Cardiff South and Penarth, Labour's Stephen Doughty won with 9,193 votes, Conservative Craig Williams was second with 3,859 and Lib Dem Bablin Molik was third with 2,103. Labour's majority was 5,334 and the turnout was 25.65%.
The first PCC elections look set to be mired in controversy amid reports of low turnout and deserted polling stations.
Total turnout in the election for the Greater Manchester police and crime commissioner has been confirmed as 13.5%.
In Wiltshire, 81,477 people out of a total electorate of 520,000 voted - a turnout of 15.8%.
After the first round of voting there, the Liberal Democrat and UKIP candidates were eliminated, with the Conservaties and Labour going through to the next round where second preference votes are included.
The Electoral Reform Society has branded the government's handling of the elections a "comedy of errors".
The society has predicted a turnout of 18.5%, which would be below the previous record low in a national poll in peacetime of 23% in the 1999 European elections.
UKIP MEP John Bufton called on Home Secretary Theresa May to resign over the conduct of the PCC elections, claiming she had ignored advice from the Electoral Commission on the vote.
But the government insists whoever is voted in will have a stronger mandate to set local crime fighting priorities than the unelected police authorities they will replace.
Counting will not get under way in Corby, Northamptonshire, until Friday morning, with a result expected at about 12:00 GMT.
The Corby contest was triggered by the resignation of Louise Mensch, the high profile former member of the Commons Media Select Committee, who stood down after just over two years as Corby's MP to spend more time with her family.
Mrs Mensch had a majority of less than 2,000 in a constituency that has regularly swung between Tory and Labour over the past 30 years - with voters always opting for the party that goes on to form a government.
She said her resignation sparked "entirely understandable local anger" and suggested that the Tories would lose the seat.