The submarines will carry the Trident nuclear deterrent when the current Vanguard class is scrapped. Theresa May said the funds will ensure the work remains on schedule.
It comes on top of £200m already pledged to the programme by the Government, giving the Ministry of Defence (MoD) an additional £800m over the coming year.
Defence Secretary Mr Williamson told the Express & Star that the funding was vital in terms of strengthening Britain's military capabilities.
"This is a welcome boost to our armed forces, ensuring we defend our country and protect our national interests with the ultimate capability," he said.
"In an increasingly dangerous world we must strengthen and maintain our ability to counter the intensifying and evolving threats we face to keep Britain safe."
Announcing the funding during PMQs, Mrs May said it was 'another sign of the deep commitment this Government has to keeping our country safe'.
She added: "This means the MoD will benefit from an extra £800 million in the next financial year and we continue to exceed the Nato two per cent target and remain the second biggest defence spender in Nato."
The funding will be viewed as another big win for South Staffordshire MP Mr Williamson, who staved off potential military cuts earlier this year by securing a new defence spending review.
Downing Street has said that current spending plans, which military chiefs had warned could see the armed forces badly diminished, will be deferred until the review was completed later this year.
Mr Williamson, who is embroiled in a battle with Chancellor Philip Hammond over military spending plans, has said he will lobby the Treasury for up to £2 billion extra a year.
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.
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.