Experts originally quoted an £89m target figure for the facility at the Faslane base in Argyll and Bute.
But yesterday, Mr Justice Coulson said the current "agreed maximum price" was around £140m. However, engineers thought the "ultimate cost" could be as much as £235.7m.
Details emerged after lawyers debated terms of a contract, drawn up when the Ministry of Defence (MoD) engaged engineering firm Amec in 2000, at the High Court in London.
The judge said the MoD and Amec could not agree on who should foot the bill.
The judge said a difficulty had arisen out of "badly-worded" contract provisions.
He decided the MoD should pay a "reasonable" amount but not costs incurred as a con-sequence of Amec's contract breaches.