But Woodward, who coached England to the 2003 Rugby World Cup, says Team GB bosses were warned this would happen.
"There have been more [appeals] than normal but we spoke to recent Olympic hosts and they all had these issues," Woodward, 56, said.
"We talked to the Australians [hosts in 2000] at length and they said it's just that as the host country you have more athletes - our team in London will be 550 compared with 300 in Beijing - so there are going to be more appeals.
London 2012 selection controversies
Tonia Couch's coach has
lodged an appeal
against the diver's omission from the individual 10m platform event.
The Cook controversy is just one of a number of simmering disputes: the sports of diving and fencing are also facing appeals from aggrieved athletes, and more discontent is expected as the remaining 300 slots on Team GB are filled.
One solution to this problem is to base selection on the most objective grounds possible, and there is no process more objective than the one favoured by the United States Olympic Committee - a system of trials in which athletes compete against each other for a place on the team.
The British boxing and canoeing teams opted for something similar to settle their own selection headaches, but Woodward does not think this approach works every time.
"You've got 26 different sports, so it's not as simple as first across the line," he said.
"There's no right or wrong way. You just need to have a process that everybody agrees to, and that process has to allow every athlete a fair chance.
"Selection is a very emotive subject. It's great giving good news to certain athletes but there are far more athletes you've got to give bad news to.
"As a coach, and I've done it, you've got to know you are picking those teams fairly, so you can live with yourself and eyeball any athlete, coach or parent, and be very clear about why you've made that selection."
Men's and women's shortlists were also announced for the road race and time trial events. Eight male and six female riders will be pared down to final selections of five and four, respectively, later this month.
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