The Tories have won 290 seats so far but can not now reach the 326 needed to win an overall majority.
Leader David Cameron said Labour had "lost its mandate to govern". Gordon Brown, whose party has 247 seats, has returned to Downing Street with aides.
Both may now turn to Nick Clegg's Lib Dems, who have so far won 51 seats, to try to form a coalition government.
The BBC projection suggests David Cameron's Conservatives will have 306 seats. If there are 10 Unionists elected in Northern Ireland then Mr Cameron might be able to command 316 - probably still slightly too few for him to be sure of winning a Queen's Speech.
But Labour and the Lib Dems together would have 317 seats, according to the BBC figures, which even with three SDLP MPs would still leave them at 320 - again a few votes short of a majority
In other election night news:
* Northern Ireland's first minister and DUP leader Peter Robinson has been defeated in East Belfast by the Alliance party
* The Greens have gained their first MP at Westminster - party leader Caroline Lucas in Brighton Pavillion
* Education secretary Ed Balls hung on in Morley and Outwood by just over 100 votes but former Home Secretary Charles Clarke narrowly lost to the Lib Dem candidate in Norwich South
* Jacqui Smith, who stood down as home secretary over her expenses, lost her Redditch seat to the Conservative but Hazel Blears retained her seat in Salford
* Labour's Margaret Hodge beat the BNP's Nick Griffin in Barking and Dagenham, with a 5% increase in her vote
* Esther Rantzen came fourth in Luton South, which went to the Labour candidate
* Lib Dem frontbencher Lembit Opik has lost his Montgomeryshire seat after suffering a 13.2% swing to the Conservatives
* There were angry scenes and calls for an inquiry after people were turned away from polling stations as long queues formed ahead of the 2200 BST voting deadline.
Senior Labour figures have said that under the rules of Britain's constitution, the sitting prime minister in a hung parliament makes the first attempt at forming a ruling coalition.
Business Secretary Lord Mandelson said Mr Brown had returned to Number 10, and was going to rest and "catch his breath" adding: "We have to be patient for some time more."
"It's not possible to make definite claims or reach final conclusions about the outcome of the election because there are results still to come in," he said.
"You could say the electorate have voted for change but what they haven't done is voted decisively in favour of the Conservatives."
Asked if it would be "inconceivable" to have a Labour minority or coalition government which did not have Gordon Brown as prime minister, Lord Mandelson said: "Frankly there are quite a number of permutations."
But he added it was "premature" to "start getting into hypotheses".
'Difficult times'
Shadow schools secretary Michael Gove said voters would not be "entirely happy" if Mr Brown "after a defeat like this, were to try to cling on and try to form some sort of coalition of the defeated, some sort of alliance of the dispossessed".
He said: "David Cameron has secure a larger number of votes and a larger share of the votes than Tony Blair secured in 2005 when he became prime minister. The logical next step is for David Cameron to form a Conservative-led government."
Mr Clegg - whose party have not performed as well as expected after a poll surge for the Lib Dems after the first live TV debate - cautioned other leaders against "rushing into making claims or taking decisions" which did not stand the test of time.
He urged everyone involved to "take a little time" to ensure people got the government they deserved during these "difficult times".
But he admitted it had been a "disappointing night" for the Lib Dems.
The Conservatives are predicted to take 297 seats in England, with Labour on 194 and the Lib Dems on 41. The Tories have also made significant gains in Wales - where Labour also regained their former stronghold Blaenau Gwent - but the Lib Dems and Plaid Cymru failed to gain target seats.
But in Scotland the Tories failed to make a significant breakthrough, while the Labour vote held up, with the party re-taking two seats it lost in by-elections - Glasgow East and Dunfermline and West Fife. The SNP and Lib Dems fell short of their targets.
Northern Ireland's First Minister, DUP leader Peter Robinson lost his seat in the first shock result of the night. The other main unionist leader - the UUP's Sir Reg Empey, was also defeated in South Antrim.
With 17 of 18 Westminster seats declared - the DUP have eight, Sinn Fein have four, the SDLP have three, the Alliance Party has one and one has gone to an independent.
