Police quizzed Neil Griffiths, of Ashford, Surrey, after the parents of three children complained.
The Metropolitan Police have sent a file to the Crown Prosecution Service, which will decide in the next few weeks whether to charge Griffiths with child cruelty offences, a source told Mirror Online.
The arrest is likely to shock BGT supremo Simon Cowell, 55, as well as the UK gymnastics community.
At least 15m viewers saw Spelbound win BGT in 2010 and earn gushing praise from Cowell and fellow judges Amanda Holden, 44, and Piers Morgan, 50.
The spectacular troupe had an even bigger stage in 2012 when they performed for a TV audience of 500m at the London Olympics closing ceremony.
As well as training Spelbound, Griffiths coached at Heathrow Gymnastics Club, where its senior acrobatic squad, which includes children, trains up to four hours a day and five days a week.
A source close to the inquiry said: "British Gymnastics regards Neil Griffiths as one of the best coaches in the world. He has absolutely huge influence in the sport."
A parent whose child attends the Heathrow club said: "Neil is very well-known and well respected within the club and British Gymnastics.
"He is a very powerful and influential figure. He has achieved a great deal but his training programmes are extremely tough. He is a very demanding coach."
Mr Griffiths is being investigated over allegations between 2009 and 2014, during which time he coached at Spelthorne Gymnastics Club, in Ashford, before moving to the west London club in 2010.
On Facebook, he has often written about his late night practices and gruelling schedule.
In April 2104, after his gymnasts won gongs at a tournament in Germany, he wrote: "Hard work pays off."
Spelbound, originally made up of 13 members of GB's acrobatic gymnastics team, was formed in 2009 to enter the ITV talent show.
Since winning BGT the troupe, which started at Spelthorne Gymnastics Club in Ashford, moved to the Heathrow club.
Three senior coaches, a choreographer and a dance teacher went with Griffiths.
The final four original members retired from Spelbound after the Royal Variety Performance in November 2012.
The troupe has starred at two Royal variety performances and appeared on another ITV prime time show, Saturday Night Takeaway.
Mr Griffiths trained presenters Ant and Dec, whom he had met on BGT, for a routine for their show.
A Met Police spokesman said: "Officers from Feltham Child Abuse Investigation Team continue to investigate allegations of child cruelty in relation to three alleged victims aged between nine and 15 years.
"The offences are alleged to have been committed between 2009 and 2014 and were reported to police in June 2014.
"On January 27 a man was arrested in connection with the investigation.
"He was taken into custody at a west London police station and subsequently bailed to return pending further inquiries."
Both Mr Griffiths and BGT declined to comment to getwestlondon's sister publication the Sunday People, where this article originally appeared.