Rupert Lowe said that a clean break Brexit on October 31 would see Britain pursue a "low-tax, low-regulation" economy that would strike fear into the hearts of the rest of the bloc.
He delivered the warning to the EU's chief Brexit negotiator Michel Barnier during a 40-minute one-to-one meeting in Strasbourg.
The UK is scheduled to depart the EU at the end of next month, but MPs from Labour, the Lib Dems and the SNP have joined forces with Tory rebels to try and stop Brexit in its tracks.
Following his meeting, Brexit Party MEP Mr Lowe, a parliamentary candidate for Dudley North, described Mr Barnier as a "serious political operator" who had "taken full advantage of a weak and submissive British approach".
But he said his attempts to encourage Mr Barnier to consider the possibility of a “standstill” agreement on trade in the event of no deal – which would allow time for new agreements to be formed – had met with rejection.
Mr Lowe said the move would "allow us to continue trade with our European friends on the same basis as we do now until a more comprehensive free trade agreement can be reached".
He added: "According to his team this had been discussed with the British government, however for Barnier and the EU the main concern is the protection of the single market and they view that approach as unworkable.
"We have seen this time and time again with Brussels where they will put the politics of the project above all else.
"I told him in no uncertain terms that it was time to put economics above politics, global headwinds are not looking good and now is not the time for pigheadedness."
During the meeting Mr Lowe also slammed Theresa May's withdrawal agreement, describing it as "a treaty that only a country in war would sign up to".
In a stark warning to Mr Barnier, he said that in the event of a no-deal Brexit the UK – with the right leadership – would pursue a low-tax, low-regulation economy which would blow the EU central planners out of the water.
"This is something Angela Merkel and others have warned against and it is a card we must be willing to play," he added.
Mr Lowe claimed that the economic wellbeing of the EU was being risked by raising the single market to a "level of totemic importance".
"I hope that the logic of the WTO ‘standstill’ agreement will win the day and we will see the referendum result finally honoured, but unfortunately the survival instinct of the EU’s political project may be overpowering," he added.