Cabinet Office minister David Lidington, Theresa May’s effective deputy, confirmed the vote would take place despite the government seeking to avoid it.
The announcement means a cross-party compromise on Brexit in talks between Labour and the Conservatives is now unlikely before voters go to the polls.
Amid anger at the failure to secure the UK’s exit from the EU on time, Nigel Farage’s Brexit Party is expected to win the vote by a wide margin, with the Conservatives set to fall to one of their worst results in recorded history.
Speaking ahead of talks with senior Labour figures on Tuesday, Mr Lidington said: "Parliament has had several occasions to vote on leaving the European Union.
“So far, every time there has been a majority against leaving with any particularly orderly deal, so we are engaged as a Government in talks with the opposition, and with others across Parliament, to try and find a way forward that has maximum possible support amongst politicians of all political parties.
“But what this now means, given how little time there is, is that it is regrettably not going to be possible to finish that process before the date that is legally due for European Parliamentary elections.
“We very much hoped that we would be able to get our exit sorted and have the treaty concluded so that those elections did not have to take place. But legally, they do have to take place - unless our withdrawal has been given legal effect - so those will now go ahead.”