French energy supplier EDF has estimated that the cost of completing the new Hinkley Point nuclear plant will be nearly 10% more than expected.
The company, which is the project's main backer, said the total cost of the power station was likely to rise by £1.5bn to £19.6bn.
Hinkley Point C would be the UK's first new nuclear plant for decades, but has been beset with budget problems.
An EDF review found the project could also be delayed by up to 15 months.
The firm said that would result in an extra £700m in costs, but that it hoped to avoid delays and finish the first nuclear reactor by the end of 2025.
Climate campaigners said Hinkley Point was "already over time and over budget" only nine months since being approved.
EDF is building two new reactors at Hinkley Point, which are expected to provide 7% of the country's electricity needs for 60 years.
Work is under way on the plant in Somerset after Prime Minister Theresa May formally gave it the go-ahead in September last year.
EDF said the extra costs partly resulted from adapting the project's design to meet the demands of UK regulators.
The French state-controlled energy firm is funding two-thirds of the plant, which is expected to create more than 25,000 jobs, with China investing the rest.
A government spokeswoman said: "Consumers won't pay a penny until Hinkley is built; it will provide clean, reliable electricity powering six million homes."
The cost of building Hinkley Point, including any overruns, will be met by EDF and the other backers, she said.
John Sauven, executive director at Greenpeace UK, said: "Hinkley is already over time and over budget after just a few months of building work.
"Today's news is yet another damning indictment of the government's agreement to go ahead with this project."
EDF said it remained on track to meet the project's first major milestone in 2019 but that delays could come later in the project.
Last month, public auditors called the new nuclear plant "risky and expensive".
The National Audit Office said the government had "increasingly emphasised Hinkley Point C's unquantified strategic benefits, but it has little control over these and no plan yet in place to realise them".
Hinkley Point C timeline
2007: EDF boss predicts UK households will cook their Christmas turkeys in 2017 using power from Hinkley Point C
2008: The project is earmarked by the Labour government as a potential site in a "nuclear renaissance"
2013: The Conservative-Liberal Democrat coalition government approves construction of Hinkley Point C and agrees commercial terms with EDF
2015: EDF signs a deal with China's state-owned nuclear firm CGN to help finance the project
March: EDF finance director quits ahead of a final investment decision on the plant
July: Theresa May delays the final decision on Hinkley shortly after becoming prime minister
September: The Conservative government approves Hinkley and signs a deal with EDF and CGN
July: EDF estimates the project will cost an extra £1.5bn and could be delayed beyond 2025 - eight years after its original target