Mrs May replied: "I can announce today the Chancellor and I have agreed that the Ministry of Defence will have access to £600 million this coming financial year for the MoD's dreadnought submarine programme.
"Today's announcement will ensure that the work to rebuild the UK's new world class nuclear submarines remains on schedule and it's another sign of the deep commitment this Government has to keeping our country safe.
"And along with the £200 million carry forward agreed at the supplementary estimates, this means the MoD will benefit from an extra £800 million in the next financial year and we continue to exceed the Nato 2% target and remain the second biggest defence spender in Nato."
HMS Dreadnought, as well as being the lead boat, will also be the class name for the Royal Navy's four new vessels which are planned to enter service in the 2030s.
Nine Royal Navy ships have borne the name Dreadnought, meaning 'fears nothing', including Britain’s first nuclear-powered submarine which was launched 56 years ago.
Work on the new vessels, which will carry the UK's nuclear deterrent after the retirement of the Vanguard submarine fleet, is already underway in Barrow-in-Furness.
The boats will be 152.9m (501ft) long, three metres longer than the Vanguard class, and will displace 1,300 more tonnes.
For the crew, there will be separate quarters for female sailors, a dedicated gym compartment, a study area and a lighting system that will imitate night and day - making it easier for the crew to get used to normal life after three months underwater.