Pressure was building on Sir Dave Brailsford to resign from his position as head of Team Sky following the news that they face another major anti-doping investigation.

The head of cycling’s governing body claimed the findings of a parliamentary committee report may damage the sport’s credibility. The UCI president, David Lappartient, called for the organisation’s independent integrity division to investigate Team Sky.

“We have the Cycling Anti-Doping Foundation, they have the power of investigation. I would like them to do this, to see if there is some violation of anti-doping rules,” he said.

The Frenchman urged further investigation after a report by the digital, culture, media and sport select committee this week concluded that Bradley Wiggins, and possibly support riders at Team Sky, had abused the anti-doping rules in the buildup to the Briton’s 2012 Tour de France victory.

MPs found Wiggins had taken the powerful corticosteroid triamcinolone not to treat a legitimate medical condition but to improve power‑to‑weight ratio. They claimed that performance-enhancing benefits would have been experienced even during the race.

Before three Grand Tours Wiggins had obtained therapeutic use exemption forms, effectively a doctor’s note, to allow him to take triamcinolone, which would usually be banned. Lappartient said the rules around TUEs had been tightened but called for another inquiry to establish whether Team Sky, led by Brailsford, had committed anti-doping rule violations.

“They had at the time the TUE agreement but now we have the evidence that it seems to be organised,” Lappartient told the BBC. “Just by a letter of support from the doctor, then it was not so difficult to get the TUE, which is something completely different now. So you have to put this in the context of the time; the grey zone was too big and it seemed that this grey zone has been used by Team Sky at the time so, is it doping? Is it just using the rules?”

The former Team Sky coach Shane Sutton, who claimed Wiggins had crossed an ethical line with his use of triamcinolone, called on the five-times Olympic champion and the former Team Sky doctor Richard Freeman to come forward with more details.

Lappartient said: “I think we need to know more about all these stories. There are still some grey zones, even in this report. I read the press release from Team Sky say ‘look we apologise, we recognise that we made some mistakes’. A mistake is something you’ve done without an intention to be wrong. The report is a little bit different.

“It seems that it was a little bit organised, so it’s maybe not a mistake but a fault, which is different, because that could affect the credibility globally of our sport and that’s why I’m concerned about this.”

Brailsford has remained tight-lipped since the report was published but calls are mounting for him to resign as team principal and even disband the team which he helped to form in 2010.

Team Sky are also in the midst of challenging a failed drug test by Chris Froome. The four-times Tour de France winner gave a urine test at the Vuelta a España last year which showed double the permitted amount of the asthma medication salbutamol. Froome has continued to ride as his legal advisers have battled to clear his name with Wiggins strenuously denying any wrongdoing when he spoke to the BBC in the week. But Lappartient said it would be a disaster if he was at the Tour de France start line with the case still unresolved.

“Of course we have to respect the rights of Chris Froome to defend what he thinks and what he believes with experts. So that’s why it’s taking some time,” Lappartient said. “I’m not sure we can have the decision before May’s Giro d’Italia – I hope we can have it at least before the Tour de France in July because, can you imagine if he’s riding the Giro and with spectators crying against him, or if at the end he’s disqualified from the Giro – that’s something difficult for our sport.

“If he rode at the Tour it would be a disaster for the image of cycling, even if on a legal point of view he has a right to ride. For the image of our sport that could be a disaster and I don’t want to put our sport into trouble. So even for him to be more concentrated on defending his own case, from my point of view it would have been better for him not to ride.”

In a statement, Team Sky said: “Team Sky is happy to co-operate with any investigation by the UCI and we would welcome further scrutiny of the Select Committee’s report. While we have acknowledged past failings, we strongly deny the very serious new allegations about the use of medication to enhance performance, as does Bradley Wiggins.

“Furthermore, we are concerned that the Committee presented these unsubstantiated allegations without providing evidence to support them, which is fundamentally unfair to the Team and its riders. “We welcome any review by the UCI which can help establish the nature of the evidence relied on by the Committee in coming to its conclusions.”

Meanwhile, Lizzie Deignan spoke of her hurt that drug-taking in professional cycling meant all riders suffer by association. “There’s lots of good, hardworking, honest people within the sport and lots of progression has been made so its damaging that has been overshadowed,” she said. “It’s definitely very frustrating and very upsetting.”