The UK looks on course to reject a change to the voting system - a major blow to Lib Dem leader Nick Clegg after his party's heavy election losses.
Almost all constituencies to declare so far have backed the current first-past-the-post system over AV.
The Lib Dems, who backed AV, lost nearly half their councillors in English local elections, with many seats going to Labour.
The SNP won a majority in the Scottish Parliament, the first party to do so.
And Labour failed by one seat to take a majority in the Welsh Assembly.
Counting is underway in the UK-wide referendum on whether to end the first-past-the-post system for Westminster elections and replace it with AV - with the final result expected at about 2000BST.
Polls suggest voters will reject change by a sizeable margin - so far almost all constituencies to declare have voted no.
Elections expert Professor John Curtice said it looked as though the eventual No lead will be of the order of 70% to 30% and although there are still lots of results to come the No campaign could "confidently look forward to success".
In the most significant test of public opinion since last year's general election, parties face the voters' verdict across the UK.
* The SNP has won enough seats in the Scottish Parliament to rule as a majority government. Scottish Labour leader Iain Gray has said he will stand down
* Labour has failed by one seat to win a majority in the Welsh Assembly
* The Lib Dems have suffered heavy losses in England but the Conservatives have avoided a similar fate to their coalition partners even making gains in some parts of the country
* The DUP and Sinn Fein are expected to remain the biggest parties in the Northern Ireland Assembly, where counting is under way
Leading Yes campaigners have already conceded defeat. Lib Dem minister Chris Huhne told BBC News: "If the boxes are anything like what I've seen it doesn't look good for the Yes cause."
And former Labour cabinet minister Lord Mandelson said: "It's going to be a very decisive no vote - I think that's very disappointing."
Turnout figures from eight of the 12 regional counting centres suggest more people than expected bothered to vote in a contest that the rival campaigns both conceded had failed to capture the public's imagination.
Turnout ranged from 35% in London - where in contrast to other parts of England there were no local elections on Thursday - to 50.7% in Scotland.
A No vote would come as a further blow to Nick Clegg, who has faced calls to quit from some of his own councillors after the party had the worst election night in its history, losing many seats to Labour.
Mr Clegg told the BBC the Lib Dems were facing "the brunt of the blame" for coalition spending cuts, adding that, for some voters, they were bringing out "memories of things under Thatcher".
He promised to "redouble our efforts" and "get up and dust ourselves down".
The Lib Dems have lost almost half their councillors in results declared so far, with many seats going to Labour. The Tory vote is holding up.
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image of Ross Hawkins Ross Hawkins Political correspondent, BBC News
Robust. Businesslike. A partnership of the head rather than the heart.
That is how senior Lib Dems are describing the coalition now.
In Lord Ashdown's words "it will never again be glad confident morning" in the coalition.
The question now is what does that mean?
Lib Dems emphasise they are not about to present a shopping list of policy demands to the prime minister.
And Conservatives, some publicly, some privately, say they will not stomach a series of concessions to Nick Clegg to make his party feel better.
But defeated, demoralised Lib Dems will need more than tales of arguments around the cabinet table to convince them their party is benefiting from the coalition - and could win back its lost seats in the future.
* Analysis: SNP steals show amid Lib Dem woe
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Salmond hails 'trust' by Scottish voters
For the Conservatives, Prime Minister David Cameron said his party had "fought a strong campaign, based on sorting out the mess left by Labour" and that the coalition government would "work for the full five years" of this parliament.
Labour leader Ed Miliband said results in England were "sending a clear message to this government, and Liberal Democrats in particular, that there needs to be a change of direction on some of the key issues".
However, Labour fared badly in Scotland, where the ruling SNP - which currently runs a minority administration - won a majority of seats at Holyrood, making gains from Labour in particular.
Overall majority
It is the first time any party has achieved this since the 129-seat Scottish Parliament was established in 1999.
The SNP's leader, Scottish First Minister Alex Salmond, promised to push for a referendum on Scottish independence during the next four years.
Scottish Labour leader Iain Gray said he would stand down in the autumn.
In Wales, Labour won 30 assembly seats, one short of the 31 needed to gain an overall majority.
The Conservatives made gains, but Plaid Cymru and the Lib Dems suffered losses.
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WHAT HAPPENS LATER?
1600: Counting begins in AV referendum
2000: AV results expected
* LIVE: Election 2011
* Vote 2011: How events will unfold
Based on results in England so far, the BBC is projecting that Labour will have a total share of the vote of 37%, the Conservatives 35% and the Lib Dems 15%.
Elections expert Professor John Curtice said this would represent the worst Lib Dem council performance since the party was formed in the late 1980s.
Compared to last year's local elections, he added, Labour would be up by 10 points while the Tories would be unchanged.
Results are also expected later in the parliamentary by-election in Leicester South, and mayoral contests in Leicester, Mansfield, Middlesbrough, Torbay and Bedford.