The issues were raised with British authorities by Union Home Secretary Rajiv Mehrishi, who was in the UK as part of the India-UK Home Affairs Dialogue, which concluded yesterday.
Asked if the extradition of fugitive liquor baron Vijay Mallya and former IPL chief Lalit Modi were raised specifically with the UK, Mr Mehrishi said the issues that affect extradition "across the board" were discussed, rather than specific cases.
"Mr Mallya's case is sub-judice. The issues around extradition discussed during the meetings only focused on any difficulties that may arise in extradition cases in general," he he told reporters at the Indian High Commission at the end of his week-long visit.
Mr Mallya, the 61-year-old former chief of the now-grounded Kingfisher Airlines, has been in the UK since March 2016 and was arrested by Scotland Yard on an extradition warrant on April 18. The airliner owes nearly Rs 9,000 crore to various Indian banks.
Out on a bail, he is fighting the extradition case in a UK court. He had fled India on March 2 last year.
And Mr Modi, also said to be in the UK, is wanted by Indian authorities in connection with a money laundering case.
India and Britain have an extradition treaty, signed in 1992, but so far only one extradition has taken place under the arrangement - that of Samirbhai Vinubhai Patel.
During the talks Mr Mehrishi held in the UK, India raised the issue of visa problems faced by Indians, including delays in student visa decisions, the high amount charged for the UK visas and the lengthy waiting period for Indian tourist visas.
The Union home secretary held talks with Brandon Lewis, UK minister for immigration and others over the past week, most of which are not in the "public domain".
The UK raised the issue of illegal Indian immigrants overstaying in the UK.
"Approximately, the UK has been able to identify in the region of about 1,000 illegal immigrants from India a year. We made it clear that it is a matter of policy for India that anybody identified as an Indian who is illegally in the UK, we will expedite his or her return," Mr Mehrishi said.
"The only issue is about cross-checks and time taken because sometimes illegal immigrants, understandably, destroy their documents and therefore identifying them as Indians takes a lot of time," he said.
The India-UK Home Affairs Dialogue was set up during UK Prime Minister Theresa May's visit to India in November 2016.
The first meeting under the process took place in New Delhi in May and the meeting in London was co-chaired by Mr Mehrishi with UK Permanent Secretary Philip Rutnam.