The four suspects – from Doncaster, Warminster, Northampton and London – are being questioned by Scotland Yard’s e-Crime unit.
The arrests are part of a wider operation involving UK law enforcement and the FBI.
Authorities from worldwide 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 arrests, British police detained Christopher Weatherhead, 20, from Northampton and Ashley Rhodes, 26, from Kennington, near London.
Both suspects are due to appear at Westminster Magistrates Court on September 7.
Police 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 US, 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.
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.
Anonymous is known as a hacktivist group, pursuing its agenda through online attacks.
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