The next phase of the program, known as Successor, is expected later this year subject to parliamentary approval to renew Britain's nuclear deterrent.
The £201 million deal is the final large design payment to BAE under a £3.3 billion assessment phase package earmarked by the previous government for development of Successor.
"The Successor program is one of the most challenging engineering projects in the world today, and this additional funding will enable us to further mature the design." said Tony Johns, the managing director of BAE Systems Submarines.
A spokeswoman for the MoD said the prototyping effort covered by part of the contract award was aimed at ensuring that the design outputs can be used in the intended manufacturing processes
"This will involve the fabrication of some representative samples of the boat's structure, such as diesel fuel tanks, the clean reserve oil tank, the dirty oil tank and a tank for collecting the drains," she said.
BAE had previously said it hopes to start construction this year but it is not clear now when a production contract will be signed.
The defense review said expected project costs were estimated to rise from £25 billion to £31 billion with a £10 billion fund also to be set aside for contingencies.