The entire country, which has a population of 1.3 billion, was put under lockdown on 23 March with less than four hours notice, in an attempt to slow the spread of the coronavirus.
A petition to repatriate UK citizens has gained more than 25,000 signatures.
The Foreign Office said it was working "around the clock" to support British travellers and help them return home.
It said it recognised many British nationals had been finding it difficult to return to the UK due to "unprecedented international travel and domestic restrictions".
Announcing the lockdown, India's prime minister, Narendra Modi, said there would be a total ban on people leaving their homes for 21 days.
He appealed for people not to panic - but crowds quickly mobbed stores in major cities and correspondents say it is not clear how people will be able to access food and other essentials.
India has around 900 confirmed cases of coronavirus, but experts warn the real number of infections could be far higher as the country has one of the lowest testing rates in the world.
Beverley Kershaw 55, from Oldham, Greater Manchester, had been expecting to fly home on Saturday but is now stuck in Candolim, Goa.
She says her flight was cancelled with "no warning" and she now fears she will not be back in the UK on time to get the medication needed for her autoimmune disease.
She is also worried about her elderly parents in the UK.
Bethan Hall, 30 and from Brighton, is in South Goa with 22 other British citizens and says all shops in the region are closed.
"We all feel totally abandoned by the UK government," she says.
"The Germans that we are staying with are all being picked up this week and none of us can even get through to our embassy - not even the people who are here who are high risk. They seem to think it is acceptable to wait for commercial flights to resume while their people slowly starve."