Kinahan is thought to have been behind a bet-to-lose horse-racing scam in the UK in 2004, in which top jockey Kieren Fallon and others were eventually acquitted when an Old Bailey trial collapsed.
His sons Christy Junior and Daniel were also arrested in an operation involving armed police.
The crime gang is suspected of major drug trafficking into the UK and the rest of Europe, gun supply to inner city gangs in Britain and several underworld murders.
The network is also accused of offering rival villains a money-laundering service to disguise their crime profits, much of it ploughed into building projects.
Several Spanish lawyers were arrested on suspicion of their part in the money-laundering side of the gang's business.
Another man arrested was Irishman John Cunningham, considered to be Kinahan's right-hand man.
Cunningham has a previous conviction for the kidnap in 1986 of heiress Jennifer Guinness in Ireland.
The principals are thought to have been under surveillance for a year or more, during which time they were overheard talking in code.
They allegedly used "computers" for guns, "waiters" for weapons, "cars" for ecstasy and "leaves" for banknotes.
If charged they are expected to stand trial in Spain and those arrested in the UK and Ireland could be extradited here.
Soca's Trevor Pearce said: "The scale of this joint operation by law enforcement agencies from so many countries is an indication of how prolific we think this network was.
"Today's arrests will have dealt a major blow to an organised criminal business suspected of supplying drugs and guns to gangs in cities across the UK and Europe.
"It highlights Soca's role in co-ordinating complex investigations into organised crime, which always has an international dimension."
