Vijay Mallya is accused of money laundering and violating the FEMA.
The UK Home Secretary will have to sign Mallya's extradition order within two months. However, Mallya's defence team has a chance to appeal in higher courts in the UK against the verdict.
Vadra is expected to be questioned again on either Friday or Saturday.
The Central Bureau of Investigation had registered an FIR on May 15, 2017 alleging irregularities in the Foreign Investment Promotion Board clearance granted to the media group for receiving overseas funds of Rs 305 crore in 2007 during Chidambaram's tenure as finance minister.
The ED said that Chidambaram has remained evasive and therefore grant of pre-arrest bail at this stage would be highly detrimental to the investigation.
India changed its stance towards Britain over Lalit Modi who has ED cases against him, and Vasundhara Raje, who gave the ruling BJP its most triumphant victory in Rajasthan, is in the dock for alleged nepotism.
The father-son duo are in the radar of the probe agencies in another case concerning the Aircel-Maxis deal.
The proclamation was issued by a special anti-money laundering court on June 14 under Section 82 of the Criminal Procedure Code
Vadra was directed by a Delhi court to cooperate with the investigation being carried out by the central probe agency after he knocked on its door seeking anticipatory bail in this case.
By registering the fresh case, ED wants to strengthen its probe against the beleagured liquor baron and expedite a slew of actions it has initiated against him
The court has now posted the matter for further hearing on May 15.
In a first, the Enforcement Directorate on Tuesday registered a money laundering case against ten people, including chief of banned militant outfit Hizbul Mujahideen Syed Salahuddin, for alleged cross-border funding of terror activities in the country.
A Delhi court on Saturday sent former Air Force Chief S P Tyagi, arrested in Rs 450 crore Agusta Westland bribery case in procurement of 12 VVIP helicopters, to police custody for four days after the CBI said he was needed to be quizzed to unearth a "very large conspiracy having international ramifications".
Gurucharan Singh's Dhawan Creative apparently clocked trades 10 times its capital in a few months.
The Enforcement Directorate has managed to sniff out over Rs 9,000 crore as suspected haul from money laundering in a decade, but it has yet to link those against anyone successfully in a court.