Detectives have been granted until Tuesday to hold the trio at the high-security Paddington Green police station in London.
"We got an extension which expires on May 6," a Metropolitan Police spokesman told AFP.
The trio were arrested on suspicion of the "commission, preparation or instigation of acts of terrorism" in dawn raids Tuesday.
Two men aged 39 and 46 were arrested at separate addresses in Newtown, central Wales.
A third, aged 33, was held in Mitcham, southwest London.
The Liberation Tigers of Tamil Eelam, who are fighting for a separate Tamil state in the north and east of Sri Lanka, are designated a proscribed terrorist organisation under Britain's Terrorism Act 2000.
Government officials and senior police officers believe large sums of money are collected in Britain to fund attacks in Sri Lanka.
Tamil Tiger activists are also suspected of involvement in widespread credit card scams, fraud and extortion.
The arrests were the latest development in a lengthy