The head of the French company that is buying GM's Vauxhall and Opel's operations for £1.9bn has said future jobs rely on improving performance.
PSA's chairman, Carlos Tavares, sought to calm fears of plant closures but said it was up to workers to build profitability.
The UK factories at Ellesmere Port and Luton employ about 4,500 people.
The Business Secretary, Greg Clark, said he was "cautiously optimistic" about the future of Vauxhall.
"The conversations that I and the Prime Minister have had, both with GM and PSA, tell me [PSA] intend to safeguard the plants, honour their commitments and look to increase the performance and the sales of cars.
"We want to hold them to those commitments, but the messages we've had lead me to be cautiously optimistic." He added.
With GM's Opel and Vauxhall operations, PSA Group will become the second largest carmaker in Europe, behind Volkswagen.
PSA also own Peugeot and Citroen.
GM Europe has not made a profit since 1999, but Mr Tavares promised to get the business back in the black once again.Image copyright Opel
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In a statement, Mr Tavares, said: "We are confident that the Opel/Vauxhall turnaround will significantly accelerate with our support, while respecting the commitments made by GM to the Opel/Vauxhall employees."
PSA said it expected to make savings of £1.47bn per year by 2026, with most of the cuts made by 2020.
Mr Tavares told the BBC that he trusted the Vauxhall staff to work in a "constructive manner" with PSA to improve their performance.
"As long as we improve the performance and we become the best, there is no risk they should fear."
'Day and night' fight
One worker at Vauxhall's Ellesmere Port plant in Cheshire told reporters this morning: "I think the deal is good for current GM and Vauxhall employees, but is there a future for younger workers after 2021?"
Next year PSA will decide where it will make the next generation of Astra cars currently made in the UK against the background of Brexit negotiations.
Len McCluskey, general secretary of Unite, said that the union would continue to "work day and night" to fight for Vauxhall staff at plants at Luton and Ellesmere Port.
Vauxhall workers 'in the dark'Media captionPSA boss: 'I trust Vauxhall workers to improve their performance'
Thousands more workers are involved in Vauxhall's showrooms and supply chain.
"The current (Astra) model in Ellesmere Port goes up to 2020/2021 but really it's this time next year, maybe the middle of next year, (when) we would need to secure acceptance of a new model there.
"That's really the challenge for all of us.
"My call to the government is to make certain that our government is at the table, just as the French and German governments will be, batting for their workforce," Mr McCluskey said.
GM chairman and chief executive Mary Barra said it had been a difficult decision to sell Opel and Vauxhall, and insisted the business would have broken even in 2016 had it not been for the UK's decision to leave the European Union, which caused a sharp drop in the value of the pound.
But the Business Secretary, Greg Clark, said the deal had nothing to do with Brexit: "This is a restructuring of the organisation. In my discussions with PSA, the chief executive said today that Brexit isn't an essential driver of this."
"We want to have the best possible trading relationship with Europe, but in any event Carlos Tavares has said that there are opportunities post-Brexit."
Former Business Secretary Sir Vince Cable expressed concerns about jobs because of the government's "lack of commitment to the customs union and the single market".
"Car components have to go backwards and forwards across frontiers and they will acquire tariffs and checks.
"And Vauxhall is particularly exposed to this, [as] about 80% of its exports are to the European Union.
"And if you're a hard-headed car executive looking at the competitiveness of Britain versus German plants, Britain, I'm afraid, is going to slip down the ranking in future."
Professor Christian Stadler, of Warwick Business School, said: "I would expect job cuts. PSA has done it before and there is no other way to realistically achieve the cost savings they have in mind, which might possibly mean plant closures as well.
"Whether this is a Vauxhaul/Opel plant or a Peugeot plant is hard to say at the moment."
AnalysisImage copyright PA
Simon Jack, BBC business editor
PSA Group says it will cut costs to increase profits, which has stoked concerns for more than 4,000 Vauxhall jobs in the UK.
The new owners met government and unions last week and provided assurance that existing production commitments would be honoured at Ellesmere Port till 2020 and Luton for some years beyond that.
However, it is generally accepted that the 24 factories the combined company will have in Europe is too many.
The deal is an exit from Europe for GM which has lost billions here since the turn of the millennium. It will allow them to focus on its home market of the US and its expanding operations in China.
PSA has said many countries are reluctant to buy French cars and the Opel brand will help them expand into new markets.
The chancellor will have extra motivation to be supportive of the car industry when he delivers Wednesday's Budget. He is expected to announce investment in skills, research and development around electric car technology in which PSA has so far lagged behind its rivals.