An internal review of the project by senior executives at EDF confirmed that the project cost has risen by £1.5bn to close to £20bn.
The review, less than a year into first construction works, also found the project could be delayed by up to 15 months. Although it said it was still aiming for HPC to start generating by the end of 2025.
It blamed adapting the design to the requirements of British regulators for part of the rise.
An EDF statement said: “The milestone for the first nuclear safety concrete for the building of Unit 1, scheduled for mid-2019, is confirmed, assuming that the final design, which is on a tight schedule, is completed by the end of 2018.
“Project completion costs are now estimated at £19.6bn in 2015 prices, an increase of £1.5bn, compared to previous evaluations.
“This estimate includes successful operational action plans, in partnership with suppliers.
“The estimated additional costs result mainly from a better understanding of the design adapted to the requirements of the British regulators, the volume and sequencing of work on site and the gradual implementation of supplier contracts.”
EDF added that there was a chance of £700m in further costs if construction fell behind.