An airline is set to investigate reports that it asked passengers to pay £20,000 towards the cost of fuel to complete their journey to the UK.
Passengers said they were asked for the money when a flight with Austrian airline Comtel Air from Amritsar in India stopped in Vienna to refuel.
Other passengers have been stuck in India after flights were cancelled.
The airline said it would investigate the claims and hoped to swiftly return people to the UK from India.
Bhunpinder Kandra, director of passenger services for Comtel Air, said: "I have heard what happened, it shouldn't have happened, and I will investigate why it happened.
"The people who had to pay the money will receive a refund."
Reena Rindi, who was on the plane with her two-year-old daughter, told Channel 4 News: "We wanted to go home. We'd been stranded for about three to four days. Who was going to take us home?"
She said passengers agreed to pay in order to fly to Birmingham.
"If we didn't have the money they were making us go one by one outside in Vienna to get the cash out," she added.
Another woman who flew from Amritsar to Birmingham via Vienna told the BBC: "We had to pay 150 euros last night in Vienna to get back to Birmingham and then they wouldn't fly us back to Birmingham so we had to pay ourselves to come back."
Comtel Air introduced cheap flights from Birmingham to Amritsar in the Punjab, via Vienna, last month.
Birmingham Airport, which said the airline had been operating successfully to Amritsar, expressed concern and added that it had started an investigation.
Mr Kandra said he hoped the situation would be resolved "within the week" and that a flight would be leaving Amritsar for the UK on Friday.
Amarjit Duggal, from Great Barr in Birmingham, flew from Amritsar last week after scattering her mother's ashes.
She said her father, sister and uncle were still there and did not know when they would be able to return home. She said it was very distressing as they were still in mourning.
"They were due to leave Amritsar on Sunday at 10:30 in the morning," she said. "They did not get the information as to what's happening with the airline."
Some airline customers who booked through Takhar Travel, in Smethwick in the West Midlands, told BBC News that they were concerned as they did not know if their flights would go ahead.
About 30 of the passengers who experienced problems in Vienna along with relatives of people stranded in India, went to the travel agent on Wednesday but said they were told the manager was not available. Police were called after staff became overwhelmed by concerned customers.
A Foreign Office spokesman said: "We are aware that a number of British nationals have been affected by difficulties with Comtel airlines flights from Amritsar to Birmingham via Vienna.
"We have been, and remain, in touch with the relevant authorities including the airline for clarification on how British nationals due to fly in the coming days will be affected.
"Our current advice to anyone affected is to contact their tour operator, travel agent or the airline for further information and about possible alternative arrangements. We would also advise that they monitor our travel advice for India for any updates.
"We took a number of calls from distressed British nationals in relation to this issue and we have provided consular assistance to those who have sought it."