The Conservative party has been contacted for comment.
Last week, the OBR said the previous government “did not provide” them with all available information at former chancellor Jeremy Hunt’s last Budget in March.
The £9.5bn overspend forms the basis of Chancellor Rachel Reeves’ claim that the Conservatives left Labour with a significant “hole” in the public finances.
Asked by the committee on Tuesday how the shortfall could have happened, the OBR’s Mr Hughes said “the system very clearly broke down”, but insisted “that kind of failure will not happen again” because of processes put in place since.
The OBR works closely with the Treasury. Its role is to assess the government’s tax and spending plans and produce reports on whether the chancellors’ plans are sound.
Its judgements and forecasts are closely watched by financial markets to determine if the UK’s economic plans are credible.
Pushed on whether the Treasury broke the law over not disclosing an overspend, Mr Hughes said there may “have been a misunderstanding of how the law ought to be interpreted”.
“There is no doubt in our minds that had that information been provided we would have had a materially different judgement,” he added.
He said it “was a question for the Treasury to ask: why was information available within the Treasury and not provided to us?”
In summarising Mr Hughes’ comments, Hillier said: “The Treasury may have even broken the law in the run-up to the Spring Budget in not disclosing all the spending information.”
Shadow chancellor Hunt has previously accused the OBR of failing to act in a “politically impartial manner” by releasing its findings about the overspend on the day of the Budget last week, arguing it would help make the case for Labour’s big tax rises.
Hunt said it was “impossible to know” how much of the £9.5bn would have been compensated for by savings elsewhere.
A Treasury spokesperson told the : “At the time of the Spring Budget, we communicated to the OBR the decision that ministers would manage spending pressures by making offsetting savings. This was within the law.
“We have accepted all the recommendations put forward by the OBR in its review of the March 2024 forecast.
“This is enshrined in the new Charter for Budget Responsibility to ensure that the unfunded pressures identified at the Public Spending Audit never happen again.”
