HMS Vanguard arrived in Devonport at the weekend
But the bulk of the overspend has been due to Ministry of Defence demands for additional safety measures.
The BBC had already discovered costs of preparing the yard at Plymouth were millions of pounds higher than the dockyard operator DML was thought to have promised.
The work was also 29 months behind schedule when the first vessel for refit, HMS Vanguard, entered Plymouth Sound at the weekend.
The Armed Forces Minister, Adam Ingram, has now conceded that the final cost of upgrading facilities at Devonport is likely to be between £638m and £659 - not including VAT.
Colin Breed, Liberal Democrat MP for South East Cornwall, now wants the House of Commons Public Accounts Committee to investigate.
It is understood DML is still waiting for full clearance from the Nuclear Installations Inspectorate to begin the refits, after inspection of its facilities.
Anti-nuclear demonstrators and supporters of the refits lined Plymouth Hoe to watch HMS Vanguard make her way up the Hamoaze at the weekend.
The Trident work is estimated to be worth £750m a year to the economy of Devon and Cornwall.
Scottish battle
The nuclear inspectorate has given only partial approval of facilities and procedures at Devonport - though enough for the first refit to take place.
In December it also emerged the base had failed a nuclear safety test.
Devonport won the contract to refit the Vanguard-class Trident submarines in 1993, despite a fierce battle by union leaders to keep the work at Rosyth.
Unions told the Conservative government the transfer plan was deeply flawed.
Devonport has the largest military dockyard in Europe, covering 650 acres on the River Tamar, on the Devon-Cornwall border.
It is already home to Trafalgar-class nuclear-powered submarines, and is now the sole refit base for the Royal Navy's underwater fleet.