The Prime Minister said locations outside London should be considered as a review is under way on how to handle repair works, which some estimates state could cost £6 billion.
In a letter to people involved in the review, Mr Johnson wrote: “Costs should be kept to a minimum (ie no gold plating). We should also move as quickly as possible.”
The PM said that the case for both Houses staying in place should be considered but that other locations should be in the mix.
He stated: “However, the review should also consider a possible location outside London.
“The Government is considering establishing a Government hub in York and it would therefore make sense to consider this as a potential location.”
His comments came after a new consultation process was launched last month which considered whether MPs and peers would need to vacate the historic building as work is carried out.
The PM said: “We should also move as quickly as possible, both because of the risks associated with the current state of the building and the need to provide certainty on the way forward and thereby minimise disruption to our business.”
Before Parliament voted in 2018 to approve the renewal works, which will entail decanting the whole building for at least six years, MPs had pushed rival plans that would have seen only a partial vacating required.
This would have forced builders to work around the Commons schedule.
The idea has since gained traction again following the coronavirus outbreak.
A recent report by the National Audit Office (NAO) stated that the £4 billion cost previously reported for the project was likely to be a “median” figure, with the final outlay on the Unesco World Heritage Site expected to be higher.
Initial estimates put the final bill as high as £6 billion, with the builders expected to be in until the 2030s.
The body said that a team will assess whether a recommendation made in a report four years ago that all MPs and Lords should leave the Palace of Westminster while the work was carried out is still the “best and most cost-effective” option.
Under the previously agreed plans, MPs are expected to move to Richmond House, the former home of the Department of Health, while the Palace of Westminster – with a floorplate the size of 16 football pitches and containing 1,100 rooms, 100 staircases and three miles of passageways – is being restored.
Parliament authorities spent £369 million maintaining the estate between 2015-19 and have predicted that costs will increase further without significant restorative works, with jobs identified including removing asbestos from 1,000 locations and repairing falling masonry.
The sponsor body is expected to report its findings in the autumn.
The NAO called for a tight grip on expenditure for the project in its April report.