The row between Jeremy Corbyn and Virgin Trains rumbled into its second day today as the Labour leader was pushed on the details of what happened on his controversial journey to Newcastle.

Corbyn answered questions tersely on the subject, reinstating his commitment to nationalise the railways, as inquiries began into Virgin Trains’ handling of the CCTV footage it published yesterday.

Meanwhile, leadership rival Owen Smith said that from the footage he had seen it appeared Corbyn “chose to sit on the floor for the purposes of the video”.

Several newspapers splashed on the story this morning, but Corbyn appeared highly frustrated when asked about the topic during a press conference for his NHS announcements today. After agreeing to talk about the subject, the Labour leader remained caustic on the topic of rail privatisation.

“I am very pleased that [Virgin owner, Sir] Richard Branson has been able to break off from his holiday to take this issue seriously and with the importance it obviously deserves,” Corbyn said. “I hope he is very well aware of our policy, which is that train operating companies should become part of the public realm, not the private sector.”

He explained that he had not chosen to take some empty seats because he wanted room to sit with his wife. “Yes, I did walk through the train. Yes, I did look for two empty seats together so I could sit down with my wife, to talk to her. That wasn’t possible so I went to the end of the train.”

However, according to the Mirror, one of the leader’s spokespersons denied this version of events, calling it “nonsense”.

Sam Tarry, a manager on Corbyn’s re-election campaign, told the Today programme that the political implications of Branson’s actions were uncomfortable. “It is quite astonishing that a tax exile of more than 10 years decides to lay into and make a political intervention – which is essentially what this is – on social media in a very public way,” Tarry said.

“I think it’s quite clear – Richard Branson is literally laughing all the way to the bank at the British taxpayer’s expense.” He added: “No train operating company in this country would be able to actually turn a profit without the vast subsidies from British taxpayers.”

The Information Commissioner’s Office, a data watchdog organisation, has confirmed it will be looking into whether Virgin Trains acted appropriately in publishing the CCTV footage.

A spokesman said: “All organisations have an obligation to comply with the Data Protection Act and must have legitimate grounds for processing the personal data they hold.

“Where there’s a suggestion that this hasn’t happened, the ICO has the power to investigate and can take enforcement action if necessary.”

Smith has said he believes Corbyn was making a “legitimate point” about rail renationalisation, despite saying it is “clear” that he could have had a seat had he wished.

“What is clear from the footage I’ve seen is that he had a seat on the train and there were seats on the train and he chose to sit on the floor for the purposes of the video,” Smith told the BBC.

“But I do think he was trying to make a legitimate point. Trains are overcrowded and I think we should be nationalising them in order to make sure they serve the British people rather better.”