Commons Leader Mark Spencer announced the controversial legislation has been scheduled to receive its second reading on Monday, June 27.
Sir Jeffrey hailed the move as “welcome and sensible”.
“It is important that this Bill now progresses rapidly through its legislative stages in the Commons before the summer recess,” he said.
While others have opposed the Bill, Sir Jeffrey has argued that, if enacted, it can help to restore the political equilibrium in Northern Ireland by replacing the Protocol with arrangements that restore the region’s place within the UK.
The UK Government has argued the measures to remove checks on goods and animal and plant products travelling from Great Britain to Northern Ireland are necessary to safeguard the Good Friday Agreement and peace and stability.
The imposition of checks between Great Britain and Northern Ireland in order to keep an open border with Ireland has angered unionists.
But capitals across the EU bloc reacted with outrage to the plans to override parts of the protocol, which governs trade between Great Britain and Northern Ireland.
The DUP has long opposed the protocol and is refusing to enter the powersharing institutions at Stormont until issues with the post-Brexit settlement for the region are addressed.
Sir Jeffrey has encouraged MPs to back the protocol Bill, saying talks between the UK and the EU have “failed to deliver solutions to the fundamental everyday problems brought about by the protocol”.
“It is important that this bill now progresses rapidly through its legislative stages in the Commons before the summer recess and we will want to see that not only does the bill receive substantial support at Westminster, but that it is not subject to either wrecking amendments or indeed other amendments that would dilute the framework and impact of the bill,” he said.
“We want to see the Northern Ireland Assembly and executive restored and that can be achieved when there is a sustainable basis for doing so.
“We will continue to be condition and not calendar led as we look forward to this bill now making rapid progress.”
Next week’s business in the Commons will also include Labour-led Opposition Day Debates on June 28 and the first day of the committee stage of the Northern Ireland Troubles (Legacy and Reconciliation) Bill on June 29.
The second day to consider the remaining stages of this Bill are expected on July 4, according to Mr Spencer.
Backbench business debates on Iran’s nuclear programme and 50 years of Pride in the UK will take place on June 30.