Kuntal Patel, who works at Barclays Bank in Canary Wharf, has reportedly been under arrest since Sunday after her home in east London was raided by the Metropolitan Police's Counter Terrorism Command.
She is the daughter of magistrate Meena Patel, who sits on the bench at Thames Magistrates' Court in east London.
"A 36-year-old woman (B) arrested on 26 January on suspicion of an offence under the Anti-terrorism, Crime and Security Act 2001 remains in custody at an east London police station...We are not able to discuss further at this stage," a Met Police statement said.
"Inquiries are ongoing as part of an intelligence-led pre-planned operation," it added.
Ron Manley, a local councillor who has known the Patels for more than 20 years, described them as an "upstanding family".
"Meena is a magistrate and used to work for a local authority, Kuntal works in the City and her younger daughter Poonam is a pharmacist.They are a Hindu family and I've known the two girls since they were at primary school. They have always been very polite, very nice girls," he told 'The Daily Telegraph'.
The son of Foreign Office diplomat Nicholas Sutcliffe, James, was also arrested as part of the operation earlier but has been released without charge triggering claims that counter-terror officials may have raided the wrong house. But the search operation at the Patel home remains ongoing.