The poll showed Labour would win 410 seats in the 650-seat parliament and a majority of 170, ending 14 years of Conservative-led government.
Sunak's party was forecast to take only 131 seats, down from 346 when parliament was dissolved and the worst electoral performance in its history, as voters punished them for a cost-of-living crisis, and years of instability and in-fighting which has seen five different prime ministers since 2016.
"Britain’s future was on the ballot at this election. And, if we are successful tonight, Labour will get to work immediately with our first steps for change," Pat McFadden, Labour's campaign coordinator said in statement.
The centrist Liberal Democrats were predicted to capture 61 seats while Brexit campaigner Nigel Farage's right-wing populist Reform UK was forecast to win 13.
While the forecast for Reform was far better than expected, the overall outcome suggests the disenchanted British public appears to have shifted support to the centre-left, unlike in France where Marine Le Pen's far-right National Rally party made historic gains in an election last Sunday.
It was not just the Conservatives whose vote was predicted to have collapsed. The pro-independence Scottish National Party was forecast to win only 10 seats, its worst showing since 2010, after a period of turmoil which has seen two leaders quit in little over a year, a police investigation into the party's finances and splits on a range of policies.
In the last six UK elections, only one exit poll has got the outcome wrong - in 2015 when the poll predicted a hung parliament when in fact the Conservatives won a majority. Official results will follow over the next few hours.
LABOUR TURNAROUND
Sunak stunned Westminster and many in his own party by calling the election earlier than he needed to in May with the Conservatives trailing Labour by some 20 points in opinion polls.
He had hoped that the gap would narrow as had traditionally been the case in British elections, but the deficit has failed to budge in a fairly disastrous campaign.
It started badly with him getting drenched by rain outside Downing St as he announced the vote, before aides and Conservative candidates became caught up in a gambling scandal over suspicious bets placed on the date of the election.
Sunak's early departure from D-Day commemorative events in France to do a TV interview angered veterans, and even those within his own party said it raised questions about his political acumen.
If the exit poll proves right, it represents an incredible turnaround for Starmer and Labour, which critics and supporters said was facing an existential crisis just three years ago when it lost a parliamentary seat on a 16% swing to the Conservatives, an almost unique win for a governing party.
But a series of scandals - most notably revelations of parties in Downing Street during Covid lockdowns - undermined then prime minister Boris Johnson and by November 2021 the Conservative poll lead, which had been higher than at any time during Margaret Thatcher's 11 years in government, was gone.
Liz Truss' disastrous six-week premiership, which followed Johnson being forced out at the end of 2022, cemented the decline, and Sunak was unable to make any dent in Labour's now commanding poll lead
While polls have suggested that there is no great enthusiasm for Labour leader Starmer, his simple message that it was time for change appears to have resonated with voters.
However, the predicted Labour result would not quite match the record level achieved by the party under Tony Blair in 1997 when the party captured 418 seats with a majority of 179.