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Chairman Jonathan Browning said the governing body will be making changes to be more caring to riders.
"Where there are failings we apologise," Browning told BBC sports editor Dan Roan.
He added the organisation would also address concerns raised by MPs at a select committee hearing into doping.
An investigation into the culture at British Cycling was launched last year after ex-riders complained about their treatment.
A report on the findings of the investigation is imminent.
But the governing body says work on an action plan to address any "failings" is already under way.
"Athlete and participant welfare is our highest priority," said Browning.
He said the organisation had achieved "remarkable success" in not only winning races, but bringing new people into the sport.
However, he added: "We deeply regret any instance where we have failed to deliver."
He accepted there had been "well reported" incidences where behaviour had been "unacceptable" and needed to be addressed.
"My ambition for athletes is anyone leaving the programme says 'I would recommend it to my younger brother or sister'," he said.
Browning said British Cycling was now "committed to implementing the recommendations of the independent review in full" to ensure the best possible environment in which its athletes could flourish.
The action plan aims include:
The independent review was commissioned last April by British Cycling alongside UK Sport, which provides elite funding to the organisation.
It came after former technical director Shane Sutton, who was was later cleared of eight of nine allegations, was found to have used sexist language towards cyclist Jess Varnish.
UK Sport chief executive Liz Nicholl says the independent review has "identified valuable lessons" both for British Cycling and other sports it funds.
The organisation set out its own action plan to help British Cycling, which includes "placing more emphasis on the importance of culture and duty of care".
Browning added: "Athlete development has been and will continue to be the key to our success at the highest level.
"This is not about complying to protect funding, this is about running and leading our organisation in a way that is consistent with our ambition to be a world-class governing body and a great place to work."
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The release of British Cycling's action plan comes a day after MP Damian Collins said the body's credibility was "in tatters" following a separate inquiry into doping.
MPs heard "some detailed and worrying" evidence from former British Cycling coach Simon Cope and UK Anti-Doping chief Nicole Sapstead, covering poor record-keeping of riders' medical details to the mysterious contents of a jiffy bag delivered from British Cycling to Team Sky at a race in France.
Browning, who only took on the role of chairman last month, said he had been left "really disappointed" by the hearing, adding: "We're still looking for clear answers. Not only do we need to be clean but we have to be able to demonstrate it.
"I've not come across any evidence of cheating. I've found an organisation that's changed quickly and needs to reset its priorities - it's something we are going to fix."
The head of British Cycling has apologised for "failings" following accusations of bullying and sexism against top-level cyclists.