The new National Crime Agency (NCA) is investigating UK suspects, including a man from Devon, over online illegal drugs marketplace Silk Road.
Four men were arrested last week over their alleged role in the online marketplace just hours after the suspected creator of the site was arrested in the United States, and other UK suspects are likely to be held in the coming weeks, the NCA said.
The NCA, which was launched on Monday, said it is investigating four men, one in his early 50s from Devon and the others in their early 20s from Manchester, over their role in Silk Road.
All four were arrested on suspicion of supplying controlled drugs and have since been bailed to a later date, a spokeswoman confirmed.
The NCA has warned that more arrests in the UK could follow.
The now-closed Silk Road, said to be one of the world's largest websites selling illegal drugs, branded itself an "anonymous marketplace" because users accessed the site through the "deep web" - parts of the internet not covered by standard search engines -so they can hide their identity.
But NCA director general Keith Bristow warned that those who think they can hide their identity should think again.
He said: "These arrests send a clear message to criminals; the hidden internet isn't hidden and your anonymous activity isn't anonymous. We know where you are, what you are doing and we will catch you.
"It is impossible for criminals to completely erase their digital footprint. No matter how technology-savvy the offender, they will always make mistakes and this brings law enforcement closer to them.
"These so called hidden or anonymous online environments are a key priority for the National Crime Agency. Using the expertise of over 4,000 officers and the latest technology, we will arrest suspects and disrupt and prevent their illegal activity to protect the public.
"These latest arrests are just the start; there are many more to come."
The UK arrests came after NCA officers, led by a team at the agency's Exeter branch and working closely with American law enforcement counterparts, identified several suspects who they thought were "significant users" of the Silk Road.
The investigation also hopes to look into the criminal use of the marketplace or the wider "deep web".
Andy Archibald, head of the NCA's National Cyber Crime Unit (NCCU), said: "This is only the start of a wider campaign for the NCA to tackle the 'dark' or 'deep' web and the criminals exploiting it.
"These criminal areas of the internet aren't just selling drugs; it's where fraud takes place, where the trafficking of people and goods is discussed, where child abuse images are exchanged and firearms are traded.
"Stopping this element of serious and organised crime will go a long way to protecting the public."
Dubbed "Britain's FBI", the NCA is leading the fight against serious and organised crime in the UK, tackling it under four commands: organised crime, economic crime, border policing and child exploitation and online protection, alongside a National Cyber Crime Unit.
As part of its work against threats from cyber space it will also lead a multi-agency team, working with partners from around the world, which will investigate and fight the threat to the UK from virtual currencies.
As part of the closure of Silk Road, millions of pounds worth of bitcoins - a virtual currency used to buy online goods - were also seized.
Ross Ulbricht, 29, the alleged mastermind behind Silk Road, was arrested last week after a federal investigation that started in 2011, and is due to appear in court for a bail hearing in San Francisco on Wednesday.
Ulbricht, who lives in San Francisco, denies charges that he operated the encrypted website where users could anonymously shop for drugs such as heroin and LSD.
He has been charged in New York with narcotics trafficking, computer hacking and money laundering in connection with the website known as Silk Road, which is believed to have collected more than one billion dollars (about £620 million) in revenue, and is also charged in Maryland with arranging to pay someone to kill a witness.