The suspects are suspected Islamist hardliners belonging a group known as "Ansarullah Bangla Team," more commonly referred to as Ansar Bangla.
Authorities named the British suspect as 58-year-old Touhidur Rahman. According to Rahman's passport, he was in the United Kingdom from 1990 to 2005, said police spokesman Maj. Gen. Maksudul Alam.
Rahman is suspected to be the main planner behind the bloggers' killings, Alam told CNN. The two other suspects were identified as Bangladeshi citizens Sadeq Ali Mithu and Aminul Mollik.
Roy and Das are among at least four bloggers who posted online pieces critical of Islam and were killed this year in Bangladesh.
Imran Sarker, president of the Blogger and Online Activists' Network in Bangladesh, welcomed the reported arrests. But, he said, "the level of involvement of the arrested suspects is not very clear. Members of our group are still getting death threats.
"Law enforcement agencies are not as active as we expect them to be. But the good news is: since the last killing, police have been more active (in) reaching out to threatened bloggers."
Fundamentalists vs. secularists
Dr. Ajit Kumar Singh, of the South Asia Terror Portal in New Delhi, said Ansar Bangla is a newly emerged terror group. It's said to be linked to al Qaeda in the Indian Subcontinent, or AQIS, a branch of the Islamist extremist group that formed in recent years, he said.
Ansar Bangla is "one of the most active terror groups in Bangladesh now," and was recently officially banned by the government there, he added.
"There is a battle going on in Bangladesh between fundamentalists and secularists," Singh said. "A blogger like Niloy Neel, the last one who was killed, was openly questioning fundamentalist thought. Organizations like Ansar Bangla wanted to shut him up -- and scare others into not talking."
The alleged link to the United Kingdom is not surprising, Singh added, pointing out that British citizens have been found to be involved with Islamic fundamentalism in the past. "This is not the first time or the last time. Radicalization in Britain is a major concern," he said.
The list of bloggers killed just this year in Bangladesh makes grim reading.
In February, Roy, a Bangladesh-born American blogger, was killed with machetes and knives
as he walked back from a book fair in Dhaka.
A month later, Washiqur Rahman, 27, was hacked to death
by two men with knives and meat cleavers just outside his house as he headed to work at a travel agency in Dhaka.
Das, 32, was hacked to death
with cleavers and machetes
as he left his home on his way to work at a bank in May. And less than two weeks ago, Neel was murdered
in his own Dhaka apartment.
Following his death, rights group Amnesty International urged Bangladesh's government to send a strong message
that killings aimed at silencing dissent are "despicable" and will not be tolerated.
According to Sarker, the struggle between fundamentalists and free thinkers began in early 2013, "when the liberal bloggers got united and started a movement against radicalization of the society by the militant groups.
"Before, the bloggers used to work on an individual level. When the young liberal bloggers in Bangladesh became unified and started being more vocal, the militant groups felt threatened and started threatening and killing bloggers."