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
Police are issuing appeals for a gang who attacked two men after luring them into meeting with what they thought were underage girls.
Aston Villa came from behind to shock Liverpool at Wembley and book their place in the FA Cup final against Arsenal next month
The film appears to show the executions of Ethiopian Christians on the beach in Libya. It has not been verified.