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.

Motorists saw the vehicle "tootling along" the A601 in Derby on 2 March, with one capturing the scene on a dashcam.
Officers said they had traced the owner to the Chaddesden area.
The man, who had a stroke some years ago, also offered his apologies to other road users, police said.
PC Mark Atterbury from the Chaddesden Safer Neighbourhood Team said: "Unfortunately he had been given some incorrect information about where and when he could use it that caused him to be on a road that was very unsafe for a vehicle of that type.
"Thankfully with the information we received I have been able to pay him a visit and give him the correct advice that means he will now be able to use his scooter in a safer fashion.
"He wanted me to apologise to any of the other road users who had been concerned about his actions but is now pleased to have had the correct information."
Source: Derbyshire Police
Four men have been arrested in separate parts of the UK by police investigating the hacker groups Anonymous and LulzSec.
[NEXT_CONCEPT]
An 83-year-old man spotted driving his mobility scooter on a busy city ring road has been "offered advice" by police.