The case will now be listed in the coming weeks for a hearing before a judge, where Mallya's legal team and the Crown Prosecution Service will go to reiterate factors for and against the businessman's extradition to Arthur Road Jail in Mumbai.
The latest extension until October 31 makes it more likely that the UK would have to contest the European elections next month, something none of the British political parties were looking forward to in light of the June 2016 referendum in favour of Brexit.
"The tragedy of Jallianwala Bagh of 1919 is a shameful scar on British Indian history," May said.
'The appellant (Mallya) has five business days to apply for oral consideration. If a renewal application is made, it will be listed before a high court judge and dealt with at a hearing,' a spokesperson for the UK judiciary said.
Under the current terms agreed with the European Union, the UK is due to leave the bloc by May 22 if the British prime minister's repeatedly-rejected divorce bill clears the House of Commons or crash out without any deal in place by April 12.
At a hearing before Master David Cook at the Queen's Bench Division of the court, Mallya's legal team sought a dismissal of the interim order.
May issued a statement to indicate the government's next steps a day after the House of Commons once again failed to agree on any specific alternative to her controversial EU divorce bill.
The diamond merchant, who has been behind bars at HMP Wandsworth in south-west London ever since his first bail application was rejected on March 20, can apply for a high court bail appeal at any time until his next remand hearing on April 26.
A set of new standard operating procedures have been issued by the force headquarters in Delhi for vehicle-mounted movement of troops in Jammu and Kashmir, and it has also been ordered that the 'passenger manifest discipline' for each vehicle in the convoy be strictly adhered to.
Embattled liquor tycoon Vijay Mallya claimed on Sunday that Prime Minister Narendra Modi's statement in a recent interview confirming the recovery of Rs 14,000 crore worth of his assets has fully vindicated him in his assertion of being a "poster boy" for the Bharatiya Janata Party-led government.
Clare Montgomery, Modi's barrister, made a series of offers to try and convince the judge to grant bail.
The judge fixed April 26 as the next date of hearing when he will appear via video link from jail.
The central government has already conducted an assessment of security cover given to prisoners in the Arthur Road Jail and its findings conveyed to the UK court.
Besides the passports, Modi also possesses multiple residency cards, some of them expired, but covering countries/regions such as the UAE, Singapore and Hong Kong.
Friday's hearing is expected to be presided over by Chief Magistrate Emma Arbuthnot, the same judge who had ordered the extradition of former Kingfisher Airlines boss Vijay Mallya last December.
She, however, did not name a departure date at the at the ruling party's influential 1922 Committee meeting.
"He is expected to be produced before the court for a second bail application hearing on March 29," a court official in London confirmed on Tuesday.
In a statement to formally update parliament on her European Council meeting last week where the EU agreed to a short delay to the March 29 Brexit deadline, the British PM said she remained committed to "guarantee Brexit" even if it isn't as initially planned for this Friday and would continue to lobby MPs to get the support required for another vote on the withdrawal agreement agreed with the European Union.
If the agreement, already defeated twice over the controversial Irish backstop clause, fails to clear the UK Parliament for a third time, the EU has set April 12 as the deadline for Britain to make up its mind on the next move.
While in custody and until the first hearing in his extradition case next week, Modi is likely to be held in a separate cell but may also have to share a cell with other prisoners given the overcrowding pressures.