The claim, in a letter to the Home Affairs Committee on Wednesday, said: "The latest running costs are £120 per person per night, compared with the latest average hotel cost of £140 per person per night. These running costs exclude set-up costs."
The Home Office’s permanent secretary Matthew Rycroft said te running costs “exclude set-up costs” and mean the barge “still meets the value for money test”, in a letter to committee chairwoman Dame Diana Johnson.
“When those are included, there is a total-life saving from use of the Bibby Stockholm of £800,000.”
The overall price per person changes depending on how many people are on board and the average hotel costs also “fluctuate” as the Government seeks to end the use of such accommodation.
It comes as Home Secretary James Cleverly was unable to tell MPs on Wednesday how many of the 33,085 asylum seekers identified as potentially eligible would be deported to Rwanda if flights get off the ground.
Under persistent questioning over how many of those people will end up in Rwanda, Mr Cleverly insisted the scheme remains “uncapped” but said he could not “speculate” about the figure.
“The answer is entirely dependent on other work we’re doing in parallel,” he added.
“It may well be if we’re successful with returns agreements, if circumstances in other countries change, it may well be that the figure is quite low.
“It could be nearly at that figure, but the point is the number of people that we might send to Rwanda is entirely contingent on a whole set of other work that we’re doing.”
Mr Sunak is trying to revive the policy by passing legislation deeming Rwanda a safe country and ratifying a new treaty with Kigali. The Rwanda Bill is currently making its way through a House of Lords that is hostile to the scheme.
Earlier this month, the Home Office shelved plans to procure more barges to hold asylum seekers.
Ministers last year touted accommodation vessels as a way of cutting the cost of housing migrants in hotels, which has hit £8 million a day.
But it is understood efforts to secure new barges have been abandoned amid struggles to find ports willing to take them.
It comes as the Bibby Stockholm, the only accommodation barge commissioned so far by ministers, has faced a series of setbacks.
An Albanian asylum seeker died from compression to the neck while living on board the barge moored off the coast of Portland in Dorset in December and is thought to have taken his own life.
The discovery of dangerous bacteria led to its evacuation last summer just days after the arrival of the first asylum seekers, and it remained vacant for two months.