The UK government has amended its foreign travel guidance to clarify that the Indian-made version of the AstraZeneca vaccine is an approved jab.
But it is not clear whether people from India can travel to the UK without having to self-isolate for 10 days.
With more than 721 million doses administered so far, Covishield is India's primary vaccine.
On Tuesday, India described the rule as "discriminatory" and asked the UK to stop requiring fully-vaccinated Indians to self-isolate on arrival.
At present, India is not listed as a country where people are recognised as fully vaccinated even if they've had both doses of an approved jab.
So, Indians travelling to Britain have to self-isolate as well as book and take Covid-19 tests before they are allowed to move freely.
Last week, the UK announced new rules - which will come into effect on 4 October - which mandate that travellers from a number of countries arriving in England do not have to self-isolate if they are fully vaccinated. India was not included in that list either.
Foreign Minister S Jaishankar had taken up the matter "strongly" with his UK counterpart Liz Truss, according to India's foreign secretary Harsh Vardhan Shringla.
It is "a discriminatory policy and does impact our citizens travelling to the UK", Mr Shringla told reporters. He had warned that India might take "reciprocal measures" if the UK did not address India's concerns.
Such measures generally include India imposing similar restrictions on those arriving from Britain. British travellers to India are thermally screened for fever on arrival, and provide a negative Covid-19 test. They do not need to quarantine.
A leading MP from the main opposition Congress party, Jairam Ramesh, had tweeted that the "bizarre" decision "smacked of racism".
Shashi Tharoor, author and Congress party MP, said he had cancelled a planned tour to participate in a debate at Cambridge University and to promote his new book in protest against the move.
"Why should Indians be deemed to be lesser breeds than others? It is deeply offensive that fully vaccinated Indians have to quarantine, while others who may have taken the same vaccine in other countries, do not," Mr Tharoor wrote in The Quint.
"The UK has done its image in India a profound disservice by failing to offer clarity on the question at the heart of the issue."
About 25% of adults in India have been fully vaccinated so far - an estimated 150 million have received both doses of Covishield at home.
The Serum Institute of India - the world's biggest vaccine manufacturer which makes the jab under licence from AstraZeneca - has also supplied millions of doses to countries in Asia, Africa and Latin America under deals signed with various governments and as part of the global Covax scheme for poorer countries.
Absolutely bizarre considering Covishield was originally developed in the UK and The Serum Institute, Pune has supplied to that country too! This smacks of racism. https://t.co/GtKOzMgydf— Jairam Ramesh (@Jairam_Ramesh) September 20, 2021