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The chair of the Office for Budget Responsibility is under pressure to explain how his report on the Budget was released early as a senior Labour MP called for him to consider resigning.

The early publication of the document has sparked fury among Labour MPs and ministers, with Liam Byrne, chair of the business select committee, telling the House of Commons that Richard Hughes, OBR chair, should “consider his position”.

“It’s a massive error,” said a government minister, while another called it a “huge fuck-up”.

The OBR normally releases its Economic and Fiscal Outlook — containing market-sensitive economic forecasts, policy costings and judgments on the government’s fiscal rules — after the chancellor has finished delivering the Budget.

But on Wednesday the full report was released about an hour before Rachel Reeves began speaking, sparking volatile trading on bond markets as investors sought to digest the near-200 page report.

An investigation into the release has been launched by the OBR and Hughes said on Thursday he would resign if he no longer had the confidence of the chancellor or the Treasury select committee of MPs after its conclusion.

Speaking at a conference on the Budget organised by the Resolution Foundation think-tank, Hughes said he was “personally mortified” by what happened and that he had written to Reeves to apologise and take full responsibility. 

“I have to say to the House that I seriously think that Mr Hughes needs to consider his position,” Byrne, a former chief secretary to the Treasury, told the Commons on Wednesday. “The fact that we had a leak of the OBR forecast before this House got to debate the Budget is appalling, and this uncertainty has bedevilled us.”

Torsten Bell, the pensions minister, told The News Agents podcast that “the OBR is going to have to think very seriously about what happened. That was an incredibly serious breach of the Budget process”.

Adding to the confusion about the early release, Hughes told the BBC that the document had not been published on “our webpage”, but that an “external person” had accessed the link.

But the original apology about the incident from the OBR on Wednesday said a link to the report “went live on our website too early this morning”. The link to the report, hosted on the OBR’s website, was accessible before the start of the Budget.

Asked to clarify his remarks, a spokesperson for the OBR said it had “inadvertently made it possible” to access the report.

Reuters said that the document had been uploaded to the OBR website and available to download on an unprotected link.

The link was not promoted on its website, but the UK’s fiscal watchdog had used the same web address, or URL, as previous Budget documents, changing only the date.

A Reuters reporter accessed the publicly available URL shortly after 11.30am on Wednesday.

The investigation into the release will be overseen by the OBR’s oversight board with input from Ciaran Martin, the former head of the National Cyber Security Centre. 

If the chancellor and the TSC “both conclude in the light of that investigation they are not going to have confidence in me, then I will resign”, Hughes said. This, he added, is “what you do when you’re the chair of something called the Office for Budget Responsibility”.  

Speaking on Sky News, Reeves described the incident as a serious breach by the OBR, but added: “I do have confidence in Richard and the OBR.”

Adding to the pressure on the OBR, later in the day on Wednesday it had to update its Economic and Fiscal Outlook document to correct mistakes on electric car sales and in calculations about the core schools budget.

Additional reporting by Valentina Romei