India and Britain also agreed to hold annual strategic dialogue at the level of Union Home Secretary to jointly deal with issues like terrorism, organised crimes, visa and immigration matters.
The Indian list of around 60 wanted people was handed over to Britain during the bilateral talks between Prime Minister Narendra Modi and his counterpart Theresa May.
Britain also handed over to India a list of 17 people whose custody it seeks under the Mutual Legal Assistance Treaty or against whom Letters Rogatories had been issued, official sources said.
The two countries agreed not to allow fugitives and criminals escape law and resolved to facilitate outstanding extradition requests.
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In talks between Modi and May, the issue of extradition requests figured and officials dealing with the issue from both sides were directed to meet at the earliest.
Asked whether Mallya issue figured in the talks, Joint
Secretary (Europe) in the External Affairs Ministry Randhir Jaiswal referred to the Indo-UK joint statement issued after the discussions which said the two Prime Ministers affirmed their strong commitment to enhancing cooperation under the Mutual Legal Assistance Treaty.
Michel is a British citizen and wanted by CBI while Mallya and Modi, who have made the UK their home, are wanted by the ED in money laundering cases.
"The two leaders agreed that fugitives and criminals should not be allowed to escape the law. They expressed their strong commitment to facilitate outstanding extradition requests from both sides.
"In this context, they directed that the officials dealing with extradition matters from both sides should meet at the earliest to develop better understanding of each countries' legal processes and requirements; share best practices, and identify the causes of delays and expedite pending requests," the statement said.
This is for the first time India and Britain will have such a mechanism for dealing with security issues.
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In a joint statement issued after the meeting, the two Prime Ministers affirmed their strong commitment to enhancing cooperation under the Mutual Legal Assistance Treaty.
"The two leaders agreed that fugitives and criminals should not be allowed to escape the law. They expressed their strong commitment to facilitate outstanding extradition requests from both sides," it said.
They also agreed that regular interactions between the relevant India-UK authorities would be useful for resolving all outstanding cases expeditiously.