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Ashford MP Damian Green says Michael Gove has assured him Junction 10a will be ready to take lorries by the Brexit deadline next month.
Highways England revealed last week how the opening of the £104m project is delayed, sparking fears of traffic chaos across Ashford when new customs checks are introduced at the Waterbrook truckstop in Sevington.
But Mr Green, who met with the Brexit minister on Tuesday, says he has been assured by Mr Gove that the junction will open to HGVs by October 31.
It won’t open to normal traffic, but lorries heading to the customs check will be able to use the new road system.
The government wants to use the Sevington truckstop as a checkpoint to allow lorry drivers with incorrect paperwork to pick up permits for onwards travel following Brexit, but Mr Green told the Kentish Express last week how he feared the arrival of more lorries would "run a real risk of disruption" if Junction 10a could not be opened.
He met with Mr Gove, the cabinet minister in charge of Brexit, to talk about the implications for the town this week.
In a Facebook post, Mr Green wrote: "Michael Gove has assured me that Highways England has been instructed to make sure Junction 10a on the M20 will be ready to take lorries to the transit area by October 31.
"This is vital for traffic around Ashford."
Earlier this year, Highways England said the junction would open to traffic in September, with other works continuing around the site until May 2020.
However, at a meeting of Ashford Borough Council's joint transportation board earlier this month, project manager Tom Selby revealed the delay, but said it wouldn't be appropriate to go into the details at the meeting.
Contractors are now working extended hours on the project, including Sundays and Bank Holidays, after the Secretary of State for transport granted Highways England's request.
From Saturday, crews began working an hour later each weekday - until 7pm - five hours longer on Saturdays - until 6pm instead of 1pm - and from 8am to 5am on Sundays and Bank Holidays.
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