The contents of the package has been the subject of significant scrutiny over recent weeks, but Brailsford told MPs that he was told by Team Sky doctor Dr Richard Freeman of its contents at the race.
Fluimucil, which is also known as Acetylcysteine, is a medication that can be used to loosen thick mucus, and is on the World Anti-Doping Authority (WADA) list of permitted drugs to treat coughs and sore throats.
Although not currently licensed for use in the UK, the drug was licensed for use in 2011 (with the license being revoked in 2013). However it is, and was, also available over the counter in France.
Asked for evidence that this was indeed the contents of the package, Brailsford said that there should be a paper trail to track the Fluimucil from the British Cycling medical cabinet to Team Sky.
“It [an invoice] should be there,” said Brailsford. “UKAD have all the invoices for our medical supplies. My understanding is that there is product code on each item.”
However Brailsford was keen to stress that he had no first hand knowledge of what was in the package, and was only relating to MPs what he had been told by Dr Freeman, who had requested the medication in the first place.
On the subject of therapeutic use exemptions (TUEs) which allow athletes to use banned substances to treat medical conditions, Brailsford said that the granting of TUEs was not a matter for Team Sky or British Cycling, but were purely a medical matter.
Brailsford was giving evidence to the Culture, Media, and Sport select committee as part of its inquiry into doping in sport.
“It [the granting of a TUE] is very much driven by the medical team, a team doctor,” Brailsford told MPs.
“The rider has a condition. The doctor assessing it, forms a diagnosis and then looks at the criteria you have to hit to be given a TUE, bring the athlete back to a baseline level.”
The hearing ended with Brailsford re-emphasising how badly he had handled the mystery package and TUE sagas, saying that it should never have come to the point where he was appearing in front of MPs.
“There are lessons to be learned. I have handled this situation very badly.
“But we have reviewed all our policies and how we use TUEs in the future and how do we gain and provide transparency while protecting competitive advantage.”
Earlier in the hearing, Shane Sutton told MPs that he arranged for the delivery of the package, but was not aware of its contents, while British Cycling president Bob Howden denied any knowledge of the package’s contents.