Wada chairman John Fahey has made implementation of the code his priority
Leading members of Team GB are so concerned by the revised "whereabouts" anti-doping system they may quit, a senior Olympic official believes.
Pete Gardner, chief executive of the British Athletes Commission (BAC), believes stricter rules brought in this year must be reversed.
Whereabouts is the system drug-testers use to track athletes for tests.
"The old system was difficult for some athletes but, once they got used to it, it was workable," said Gardner.
"They could fit it into their schedules and they saw value in it. But the new system is causing real problems.
"There are some athletes who are so worried about missing tests inadvertently they have said if they got to two missed tests they would seriously consider retiring before missing a third.
"They've seen what has happened to people who have fallen foul of the three missed-test rule - and how the public have reacted - and, as clean athletes, they don't want to tarnish their records.
It would be impossible for us to run a testing programme without knowing where the athletes are
UK Sport's head of drug-free sport
"We really want to speak to Wada (the World Anti-Doping Agency) about pushing those changes back to where they were before."
A revised version of the Wada code, the global standards that underpin the fight against drugs cheats, came into force on 1 January, and among the key changes was a significant tightening up of whereabouts.
Before 1 January, any athlete in his or her country's testing pool (so any elite athlete in an Olympic sport or leading players in the main team sports) would have to specify, three months in advance, a time and a place each day, five days a week, when they could be found to give a no-notice drugs test.
Athletes could pick any hour between 0500 and 2300, and they would only have to be in the stated place for a portion of that hour, the onus being on the testers to be in the right place at the right time.
Many athletes, therefore, selected 0500-0600 as their window and resigned themselves to the fact they might get an early wake-up call two or three times a year.
The new code, however, moved the earliest available time back to 0600 and crucially called for the athlete to be available for the full stated hour. The system was also extended to seven days a week.
Anti-doping bosses say without whereabouts there will be no deterrent
As a result of these changes, some athletes are concerned they could be charged with a missed test - three of those in 18 months and you are deemed to have failed a test, as Olympic champion 400m Christine Ohuruogu discovered to her cost - if they are late for a test or in the middle of a training session.
Others are annoyed they are now effectively sitting around waiting for somebody to turn up for 365 hours a year.
Gardner would not be drawn on which athletes have threatened to quit should they pick up two strikes - and you can also earn a strike for making a mistake with your online form - but they are believed to include medal-winning members of Britain's rowing squad.
News of unrest over whereabouts in the British camp comes a week after it emerged a group of Belgian professional athletes have started proceedings against their regional government on the same issue. They are challenging whereabouts as an invasion of privacy under European Union law.
Two more challenges from professional team sport also expected to whereabouts on the basis of EU data protection and working time regulations. And world tennis number one Rafael Nadal has also spoken out against the strict imposition of Wada's code.
For their part, the anti-doping authorities are adamant that whereabouts is a necessary evil.
Andy Parkinson, who runs Britain's drug-testing regime for UK Sport, said: "There is no doubt whereabouts is intrusive, but as long as it's proportionate to the risk of doping in sport then it has a very valid place.
They have gone too far, too quickly and they have not engaged with the players
Professional Players Federation
"In fact, I'd go further than that and say it would be impossible for us to run a testing programme without knowing where the athletes are."
But Simon Taylor, the general secretary of the Professional Players Federation (PPF), went even further than Gardner and said the current system was in danger of becoming a "fiasco".
The PPF, an umbrella group of professional player associations in the UK, is angry it was not sufficiently consulted ahead of the new code's introduction.
"We need Wada and we're all in favour of drug-free sport," said Taylor.
"But they have gone too far, too quickly and they have not engaged with the players. It's now a case of not if Wada will change the rules but when."
The Montreal-based anti-doping authority has recently said it will meet any organisation concerned or confused by the new code's provisions, particularly whereabouts, and Taylor welcomed that move.
"If you work with the players you'll get a stronger policy," he added. "We want to help."
Wada board member Sir Craig Reedie, however, denied the consultation process had been flawed.
The former British Olympic Association boss and current International Olympic Committee member said the code was revised after more than 18 months of talks with the sports, and pointed out that football's international governing body Fifa had been particularly involved.
"I am surprised people are coming forward within 30 days of the code coming into force so say they don't like it much," said Reedie.
"Our belief is that you should give the system a chance to settle down and then take a view after mature reflection."