Britain has asked the Indian government for more information after overseas funding for a charity founded by Mother Teresa was blocked.
India's Ministry of Home Affairs withdrew the licence for foreign funding from the Missionaries of Charity in December.
NGOs are required to have a licence to receive donations from abroad under the Foreign Contribution Regulation Act, but thousands of organisations are feared to have had their applications rejected.
During a debate in the House of Lords, Lord Harries of Pentregarth voiced concerns that Hindu nationalism was behind the actions against Missionaries of Charity.
"The work of Mother Theresa and the charity she founded, the Missionaries of Charity, is renowned throughout the world. It works among some of the poorest and most destitute people on earth," he said.
"What possible reason could the Indian government have for wanting to hinder and block its work?
"The rumour, I am afraid, is that it is continuing pressure from Hindu nationalism, because people might come into contact with Christianity and eventually convert to it.
"We need to know from the Indian government precisely, in writing, what their reasons are so that we can examine the validity of their reasoning."
Lord Alton of Liverpool warned that "there will be appalling consequences for some of India's most vulnerable people unless this iniquitous decision is reversed".
Baroness Northover said that the removal of licences was leaving NGOs in India "starved of funds", and that Britain must engage at a ministerial level to have the funds unblocked.
"Is this not what global Britain was supposed to be about: promoting UK values, including human rights?" she said.
Asked about what representations the British government has made regarding the withdrawal of the licence, minister for South Asia, Lord Ahmad of Wimbledon, said British officials had discussed the issue with the Indian government and that the British High Commission in New Delhi was monitoring developments in this respect.
"On the issue of the licence in India, I have looked into this specifically, and we do not know why its applications were rejected. I have asked and pressed to see the kinds of numbers that currently exist," he said.
"Among the 12,580 organisations whose licences have ceased to exist, some ceased to exist because they did not submit their applications in time, and others were rejected for other reasons.
"There are Christian NGOs, but there are also 250 Hindu NGOs and more than 250 Muslim NGOs, so whether this is specifically against Christian organisations is not shown by the data, but I am requesting further information in this respect."
He continued, "My Lords, we are raising these issues quite directly. Because of the constructive nature of our engagement, we are able to raise this not just with the Indian high commission here in London but in a constructive manner with the Indian government directly.
"As I alluded to earlier, I have asked specifically for a drill-down on the numbers over a period, so that I can analyse directly which organisations are impacted and the reasons why these licences have been revoked, to allow us to make much more qualified representation."