Begg, 45, who spent three years in US detention before his release without charge in 2005, was arrested by counter-terrorism officers at his home in the central English city of Birmingham on Tuesday.
A district judge on Wednesday granted a warrant of further detention until March 4, according to a West Midlands Police statement.
Outspoken rights activist Begg was arrested on suspicion of attending a terrorist training camp and facilitating terrorism overseas.
Begg had written in a blog earlier this month about making two trips to Syria in 2012 to investigate allegations of western complicity in torture.
A 44-year-old woman and her son aged 20 were held on suspicion of facilitating terror abroad, as was a 36-year-old man at a separate address, police said.
Searches continue at the three home addresses of the individuals detained in the pre-planned operation, the force added.
Begg moved to Afghanistan with his wife and three children in 2001, where he insisted that he was only involved in charitable activities, but fled to Pakistan after the US-led invasion to topple the Taliban after 9/11.
He was detained in Islamabad as an "enemy combatant" in February 2002 and taken to the Bagram prison in Afghanistan for about a year, where he said he was beaten.
US authorities released him and three other Britons in January 2005 and he was allowed to return to Britain where he was arrested by the police before being freed without charge.
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