A threat of imprisonment by parliament forced Rupert Murdoch and his son James to perform a volte face and agree to give evidence next week to a Commons committee investigating why News International executives provided false information to MPs.

Hours after the parliamentary authorities delivered a summons by hand to the two Murdochs, News International announced that father and son would accept an invitation to appear before the Commons culture select committee next Tuesday.

Rebekah Brooks, the News International chief executive, had earlier accepted an invitation from the committee, which is seeking to discover why a succession of company executives provided misleading information about phone hacking.

The capitulation by the Murdochs represents a victory for parliament and the select committee system, which is often criticised for lacking bite. The culture committee issued a summons for the Murdochs after they missed a 9.30am deadline to say whether they would attend.

Lawrence Ward, the deputy serjeant at arms, hand-delivered the summons to a lawyer at the News International headquarters at Wapping. A member of the select committee said at the time: "We have taken it to Defcon Two. Whether we go up another notch is up to the house. We have been advised that parliament could vote to imprison them."

John Whittingdale, the Tory chair of the committee, was advised by the parliamentary authorities that he could refer the matter to the Commons if the Murdochs failed to accept the summons to appear on Tuesday. MPs could then vote to summon them to the bar of the Commons – the strip on the floor of the house marking the end of the standing section for MPs – where they could have been informed of their punishment. This could have included admonishment, a fine or imprisonment, possibly in a cell under Big Ben.

The summons was issued after Rupert Murdoch said he would not give evidence to the committee until after appearing before the public inquiry chaired by Lord Justice Leveson. James Murdoch said he could not appear until 10 or 11 August. Parliament will be in recess then.

Within a few hours of the summons, James Murdoch wrote to Whittingdale to say that and his father would appear after all. But he indicated that they may not be forthcoming because they have received legal advice that they must be careful not to prejudice the police investigation into phone hacking.

James Murdoch, who said that he and his father would co-operate fully with the public inquiry to be chaired by Lord Justice Leveson, wrote: "I am, however, very much concerned that we are now being asked to answer yet further questions in a different forum. We have been advised that, in light of the fact that there are to be multiple reviews of the issues, this does carry the risk of prejudicing other judicial proceedings and in particular the ongoing police investigation and any potential subsequent prosecutions. I would therefore respectfully ask you to take the utmost care in ensuring that the committee hearing does not run any risk of prejudicing that investigation and subsequent prosecutions."

Members of the select committee said they would dismiss any attempt by the Murdochs and Brooks not to answer their questions. "None of them has been arrested and sub judice rules do not apply," one MP said.

Tom Watson, a Labour member of the committee who has led the campaign against phone hacking, told Channel 4 News: "We need to know what Rebekah Brooks knew about payments to police. We need to ask James Murdoch how he authorised payments to buy the silence of hacking victims. And from Rupert Murdoch we just need a wider question: why did you let this happen?"

Brooks was forced to write to the Commons home affairs select committee in April to say she had no knowledge of payments to police officers in exchange for information. The News International chief executive, who edited News of the World before moving to the Sun in early 2003, told the culture committee that year: "We have paid the police for information in the past."

One member of the committee said: "Our committee has been pursuing this for four years. There have been two select committee inquiries. We want to get to the bottom of who knew what and when. We have had witnesses from News International who maintained at both inquiries who said there was just one rogue reporter. Since then the News of the World has closed and it is clear that after one of our investigations in 2007 evidence emerged in which complicity was uncovered. For the integrity of the committee we need to know what these witnesses knew and when they knew it. James Murdoch admitted in his statement announcing the closure of the News of the World that untruths were told to parliament He said he did not have the full picture when payments were made to victims of phone hacking. … News Corp need to amplify on what they told us. All the figures from News International who appeared before us have left the company, apart from Les Hinton."