It said that the decision marks "a major step in the UK's nuclear renaissance" — Whitehall has said it wants to build enough new nuclear reactors to meet about a third of the UK's energy needs by 2030.
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Kier has been involved in a joint venture with BAM Nuttall to prepare the project's site since 2012, and currently has around 350 employees working on it.
This has included the excavation of over 5.6m cubic metres of material, large scale earthworks, the development of complex terracing structures and the creation of an expansive road network.
The company's shares fell 0.33 per cent to 1.220p per share in mid-morning trading.
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Kier Group chief executive, Haydn Mursell said: "Today's decision marks a major step in the UK's nuclear renaissance and reflects the country's commitment to a balanced energy strategy including low carbon energy sources.
"Kier has excellent and proven capabilities in the nuclear industry and we look forward to working with EDF on the pipeline of opportunities that will arise from this project and on further energy projects in the UK in due course."