In a statement on preparations for Britain's departure, Brussels said it would not enter talks on future trade until London honours "the financial obligations the United Kingdom has made as a member state".
This sum would cover budget commitments up through a transition period at the end of next year, but the British parliament has refused to ratify the treaty and Brexit has been delayed until October 31.
The decision is seen as a victory for former foreign secretary Boris Johnson and some of the other nine contenders bidding to succeed Theresa May as prime minister.
Johnson has suggested that withholding the funds could give Britain leverage in the divorce talks, but Wednesday's European Union statement said no such negotiations would begin if the bill is not honoured.
Brexit secretary Steve Barclay, speaking prior to the vote, said it was a "blind motion" that gave no indication as to what path MPs would try to pursue to block a no-deal departure, and would have "virtually unlimited scope".
Conservative opponents of no-deal and leadership candidates, Matt Hancock and Rory Stewart, revealed that they would vote against the motion.
Britain's businesses are being urged to step up their preparations for a no-deal Brexit amid signs that Theresa May's successor could be prepared to leave the European Union without a deal at the end of October. With business costs rising in many quarters, and management time precious, it's understandable that firms don't want to put resources towards preparing for something we still hope won't happen.
Keir Starmer, Labour's Shadow Brexit Secretary, said: "This is a disappointing, narrow defeat".
Jeremy Corbyn's plan was to take control of the House of Commons order paper to prevent a new Prime Minister from suspending Parliament to force a no deal Brexit through.
"It will introduce a safety valve in the Brexit process and it will be a reminder to all Conservative leadership candidates that this house will take every step necessary to prevent a no-deal", he added.
MPs voted 309 to 298 against the measure which would have enabled politicians to size control of the House of Commons later this month.
That has spurred some of those hoping to succeed her - including front-runner Boris Johnson - to promise that they will not delay Brexit beyond its current scheduled date of October 31.