The suspects - from Doncaster, Warminster, Northampton and London - are being questioned by Scotland Yard's e-Crime unit.
Their arrests are part of a wider operation involving UK law enforcement and the FBI.
At the same time, 14 suspected members of Anonymous appeared in a US court.
Authorities around the world have been rounding up suspects following a wave of attacks by both groups on major corporations and government institutions.
Amazon, PayPal, the CIA, US Senate and the UK's Serious Organised Crime Agency have all suffered either intrusions or denial of service attacks, designed to take their websites offline.
In the latest round of British arrests, police detained 20-year-old Christopher Weatherhead from Northampton and 26-year-old Ashley Rhodes from Kennington, near London.
The pair are due to appear at Westminster Magistrates Court on 7 September.
Detectives also arrested a 24-year-old man from Doncaster, and a 20-year-old from Wiltshire for conspiring to commit offences under the Computer Misuse Act 1990.
In the United States, a mass court appearance saw 14 suspected Anonymous members appear before a judge in San Jose, California.
All of them denied being involved in a denial of service attack on PayPal's website in December 2010.
Anonymous had publicly declared its intent to target both PayPal and Amazon for, what the group perceived as, their complicity in isolating whistle blowing website Wikileaks.
Following the leaking of confidential US State Department memos, PayPal stopped processing donations to Wikileaks, while Amazon kicked the site off its web hosting service.
Four men have been arrested in separate parts of the UK by police investigating the hacker groups Anonymous and LulzSec.