The Archbishop of Canterbury has joined a campaign to save a charity, saying its collapse will put lives at risk.
Supporters of legal charity Refugee and Migrant Justice say it will close, leaving 10,000 people unrepresented, if government does not speed up payments.
The charity says new legal aid rules mean it must wait up to two years for payments government has already agreed.
The Ministry of Justice says RMJ has had three years to prepare for the money-saving changes.
The legal charity employs more than 300 specialist staff representing some of the most complex immigration cases in the UK.
The majority of the clients are asylum seekers, but the organisation also represents 900 unaccompanied children and women trafficked against their will by organised criminals into the British sex industry.
It says it has now been hit by a massive cash flow crisis because of reforms to the legal aid system designed to cut costs and make firms in the immigration sector more efficient.
Under the new rules, bills are not finally settled until cases are completed. RMJ says it is owed almost £2m and could be waiting up to two years for payments on the most complicated.
It has sought bridging loans while it waits for the payments, but has no assets to offer as security to commercial lenders.
In a letter to Justice Secretary Ken Clarke and Home Secretary Theresa May, Dr Williams and other campaigners say: "No charity can be expected to wait six months or more for the money it is owed, and no private sector organisation will be able to replace RMJ's longstanding commitment to those with the greatest needs.
"The government has said it wants to speed up asylum decisions, but closing RMJ would be a huge backward step.
"Many asylum seekers will be unable to access good quality legal support, or any support at all. Lives will be put at risk and there are likely to be many more miscarriages of justice - which are already common in our asylum system.
"This would also add to the UK Border Agency's enormous backlog, as the cases of existing clients would have to be suspended while new lawyers are found."
Officials at the Ministry of Justice have spent almost three years working with the charity on the changes because of its recognised reputation in immigration law and they recognise there would be "disruption" were the organisation to collapse.
A spokesman said: "The resources for legal aid are finite and therefore we must make the best use of those available. Other organisations have successfully made this transition and it is only reasonable to expect Refugee and Migrant Justice to do the same."
But Caroline Slocock, the charity's chief executive, said: "RMJ is not asking for new money, simply prompt payment of legal aid by the Legal Services Commission, or failing that, interest-free loans by the government to cover the gap."