The alleged offences include network intrusion and data theft from enterprises and governments; distributed denial of service (DDoS) attacks; cyber related fraud and malicious software and virus development.
The NCA worked with local police forces across the UK to make the arrests.
25 people in the London and Essex area were arrested by the Metropolitan Police on suspicion of cyber fraud including theft and money laundering.
Five men were arrested in Kidlington, Oxford for an alleged conspiracy to commit computer misuse offences.
One man was arrested in the West Midlands on suspicion of network intrusion on the US Department of Defense.
Peter Goodman, deputy chief constable, said that cyber crime wasn’t victimless and SMEs can be bankrupted by cyber attacks. Publication of personal data could seriously affect people.
The NCA says people should go to www.getsafeonline.org and www.cyberstreetwise.com to stay up to date on how to keep your computer more secure.