With 646 of 650 seats decided by late afternoon on Friday, the centre-right Conservatives had 304 seats to the ruling Labour party's 258.
Conservative leader David Cameron said it was clear the ruling Labour party "had lost its mandate to govern".
However, Labour politicians stressed Britain's constitution gave current Prime Minister Gordon Brown the right to try to form a government first. He would struggle to do so with the third-placed Liberal Democrats, however, since their combined forecast seats would still be short of a majority in parliament.
The first inconclusive election since 1974 and uncertainty about who will form the next government is likely to trouble already febrile financial markets.
Focus has now switched to which parties enter into talks with one other. They will be assisted by civil servants who have prepared briefing documents outlining key elements of party proposals and their costs.
Liberal Democrat leader Nick Clegg has said the onus is now on David Cameron to demonstate he is capable of forming a government that can rule "in the national interest".
A sense of confusion was heightened by reports that hundreds of voters had been turned away from crowded polling stations across the country when voting ended at 22:00 local time.
Results from the 650 seats rolled in against a backdrop of global market turmoil following a huge sell-off on Wall Street and the fall-out from the Greek debt crisis.
The pound slumped against the dollar, while equity futures tumbled and gilt futures soared, with markets fretting over the uncertainty but more concerned by turmoil on other exchanges.
Minority government
An exit poll, which surveyed around 20,000 people out of around 45 million Britons eligible to vote on Thursday, suggested the centre-right Conservatives were likely to win 305 seats and Labour 255 seats in the lower House of Commons, both short of the 326 needed for a majority.
It put the Liberal Democrats, who had been expected to perform strongly, on 61 seats - surprisingly down two on their current number in parliament.
"I still think the exit poll is a good guide, but we shall have to wait [...] before making a judgment," said Andrew Hawkins, chairman of polling firm ComRes.
The results so far indicate the exit poll seems reasonably accurate.
Most seats showed a swing in support to Conservatives but, if repeated nationally, not all of sufficient size to give the party an overall majority.
Notable losses for Labour included former cabinet ministers Charles Clarke and Jacqui Smith, while Northern Ireland's first minister, Peter Robinson, of the Democratic Unionist Party, was the highest profile casualty of the night. Gainers included the Greens, who won their first ever parliamentary seat.
Britain's constitution dictates that Labour's Brown gets the first chance to form a government, but analysts said the most likely scenario was a Conservative minority government.
"[It will lead to] almost certainly a minority government led by Cameron. Cameron is going to try and get policy programmes into place, demonstrate his competence and then call a second election this autumn or next spring," said Mark Wickham-Jones, professor of political science at Bristol University.
Cameron said he would be guided by national interest in decisions made over the coming hours. However, he also said: "I believe it is already clear that the Labour government has lost its mandate to govern our country."
The next government will have to deal with a record budget deficit running in excess of 11% of national output, and demands for political reform following a parliamentary expenses scandal last year which left Britons disgusted with lawmakers.
Markets fear a stalemate could lead to political paralysis, hampering efforts to tackle the nation's spiralling debt and secure recovery from the worst recession since World War Two.
Independent think-tanks have accused all the parties of failing to be open with voters about the scale of cuts that will be needed to restore public finances, meaning any government could face a plunge in popularity early on once cuts begin.
"This might be the election you want to lose and win the next one," said Wayne Anderson, 42, who works at a brokerage in London. "It could be a poisoned chalice with a small majority or minority. It would be more difficult to make decisions in a hung parliament."
A series of three US-style leaders' television debates, a first for UK politics, energised campaigning and boosted turnout.
However, the higher turnout caused problems in some constituencies, with voters turned away from busy polling stations because election officials were unable to cope with a paperwork prompted by a late surge.
Britain's electoral watchdog said it had launched an investigation, raising the possibility of legal challenges to some results.
(EurActiv with Reuters.)
