The announcement followed the successful firing of an unarmed Trident ballistic missile by HMS Vigilant during a test launch in the Atlantic Ocean last week, according to the the MoD.
HMS Vigilant is one of four Vanguard Class submarines which maintain the UK's nuclear deterrent.
The Vanguard submarines will be replaced from 2028 by the Successor which is currently being designed by British companies.
As a result of this latest announcement, BAE Systems will proceed with an additional £315 million worth of work, with a further £38 million carried out by engineering support services company Babcock
More top news
A man and a woman have been charged with murder after a badly burned body was found in the back garden of a house in south-west London.
After a chilly start, there will be some warm sunshine across southern and eastern parts.
Labour is ready for another election after June's vote "changed politics in this country", Jeremy Corbyn has declared.