The Indian high commission announced outsourcing many of the services to VFS from March 1 with six new visa application centres around the country, taking the total up to 14.
"This is a culmination of over a decade of campaigning and I am delighted that services required by tens of thousands of people of Indian-origin will now be provided, including visa services, OCI (Overseas Citizen of India) and Indian passport services," said Vaz, MP for Leicester East - a heavily Indian-origin constituency.
The chair of the influential Home Affairs Committee in the UK Parliament said centres in cities like Birmingham, Manchester, London, Edinburgh, Belfast and Leicester will benefit thousands and the "High Commission of India can be commended for taking this important step".
However, some UK-based tour operators have expressed some concern over the new rules around biometric data collection, including mandatory fingerprint data and facial imagery.
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The Association of British Travel Agents (ABTA) warns that the move could prove off-putting to some British tourists.
"We are writing to the Indian High Commission expressing our concern about the short notice given concerning this change to visa requirements, requesting that they either reconsider or delay its introduction," said Nikki White, ABTA head of destinations and sustainability.
"We are also expressing our concerns about the requirement for individual family members to book separate appointments which could cause considerable unnecessary inconvenience and have the unintended consequence of discouraging travel to India," she added.