"There is a change within India and both sides are keen to see it happen," Chris Grayling, British secretary of state for justice said.
"It is something we will continue to push for as it is in the interests of both countries," he said during a briefing at the Ministry of Justice (MoJ) here.
The British government has been consistently pursuing Indian authorities over opening up the lucrative Indian market to international law firms.
The Indian legal sector, however, remains closed to foreign firms under strict regulations.
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Vara recently joined the MoJ as parliamentary under-secretary as part of a reshuffle by Prime Minister David Cameron.
This is the first ministerial appointment for the senior Conservative party MP from North West Cambridgeshire and a former City solicitor, who has been an assistant whip in the coalition government and shadow deputy-leader of the House of Commons.
Vara is now in charge of courts and legal aid. His portfolio also includes judicial policy, civil law and justice, international business among others.