"The project I worry about the most in relation to future financial risk is the nuclear enterprise. It's a significant element of the overall equipment plan ... it most keeps me awake at night," he told the committee during a session examining the MoD's progress in improving financial management.
The defense nuclear enterprise covers the equipment, infrastructure and people required to deliver the UK deterrent and nuclear powered submarines, including the new Astute-class hunter killer boats and Trident missile boats.
The third of an expected seven Astute-class nuclear submarine fleet recently left the BAE Systems' yard at Barrow-In-Furness for sea trials.
Thompson, one of the principle architects behind the MoD's improved control of its budgets in the last few years, said if the government goes ahead with plans to build a new generation of nuclear missile submarines, annual costs of nuclear-related work will exceed £5 billion (US $7.7 billion) a year compared with today's figure of more than £3.5 billion.
Britain's defense procurement and support spending this year is set at nearly £13 billion. Peak spending on the Successor nuclear deterrent program is expected to get underway next year and run until the late 2020s, consuming a major part of the equipment budget.
"It's the single biggest future financial risk we face. The project is a monster. It's an incredibly complicated area to estimate future costs but we will make them," he said.
The Conservative government has not given an up-to-date estimate of the program costs. Previously, it has said the submarines would cost between £11 billion and £14 billion at 2006 prices and estimated an overall cost of up to £20 billion when infrastructure and other costs are wrapped in.
In its 10-year defense equipment plan of 2014-2024, the MoD said it planned to spend around £40 billion on submarine procurement and support.
Thompson said an updated equipment spending plan covering the decade up to 2025 is likely to be published in the next couple of weeks.
The Conservative government is expected to seek parliamentary approval next year to start building four Trident missile-carrying Successor submarines to replace the same number of Vanguard-class boats tasked with providing Britain's nuclear deterrence.
The Labour Party, the main opposition party, has previously been committed to a credible nuclear deterrent, but the recent election of the left-winger Jeremy Corbyn as the party leader has thrown that policy into confusion.
Even so, the Conservatives would expect to secure approval for the program as a number of Labour Party members of Parliament would likely vote with the government or abstain.
BAE Systems and its industrial partners, Babcock International and Rolls-Royce, have been working on a five-year, £3.3 billion assessment phase ahead of an expectation of starting to cut metal on the first boat next year.
Functional engineering on the Successor is more or less complete and BAE is now into the spatial engineering phase ahead of the expected development and production go ahead in 2016.
The first of the new class of submarines is expected to enter service in 2028. Some long lead items are already being funded and infrastructure projects undertaken to allow construction and operation of the boats.
Aside from the Trident missile, Britain is collaborating with the US on a common missile compartment and associated navigation, fire control and launch systems.
General Dynamics Electric Boat already has a contract for the first 12 missile tubes destined for the Successor program.
Andrew Chuter is the United Kingdom correspondent for Defense News.