They say it is a last resort: the Asylum and Immigration Appeals Bill does not provide a legal avenue for appeal against deportation orders.
A spokesman from the Home Office said he was aware of the safe-house network but warned: 'Anyone who unlawfully harbours an illegal immigrant is guilty of a criminal offence.'
But Lee Jasper, spokesman for the National Black Caucus, says supporters are willing to defy the law to keep families together. 'The Bill contravenes the European Convention - guaranteeing people the right to a family life. Until it is amended we reserve the right to do what is necessary to protect families threatened with deportation,' he said.
Fears of forced deportations without warning have been fuelled by the recent death of Joy Gardner. Mrs Gardner died of hypoxia - the cutting of oxygen to the brain - after being restrained by police in her north London flat.
The Home Office insisted that Mrs Gardner was an illegal immigrant; her family and supporters argued that she had every right to stay in Britain.
'Joy Gardner is just one member of the black community who has fallen victim to an immigration policy which is racist,' said Mr Jasper.
'For every white person refused entry to this country, 37 blacks are refused entry. When the law leaves no room for legal challenge . . . ethnic minorities are entitled to engage in acts of civil disobedience.'
One Ghanaian family currently being hidden by the group has been threatened with deportation because an officially acknowledged postal error prevented them from renewing their visas in time.
Justice Anim, 49, the head of the family, said: 'I do not want to settle here. I am appealing to stay here on behalf of my son. I am paying for him to have medical treatment which would not be easily available at home. If they can do it for Bosnians, why can't they do it for us?'
Four years ago a similar network of safe houses was set up in protest at the deportation of Viraj Mendis, a Sri Lankan communist and supporter of the Tamil separatists.
Mr Mendis was offered sanctuary in a church in Manchester for more than two years, after claiming that he would face persecution if he returned to his home country. The Home Office eventually rejected his claims and deported him amid protests from support groups, church leaders and members of the Government.
In the aftermath an 'underground railway' sprang up. In defiance of the 1988 Immigration Act, supporters offered their homes as safe houses to families threatened with deportation, according to the pressure group Refugee Forum. Twelve churches in Newham, east London, voted to offer themselves to the cause, and a mosque offered refuge to Amir Abdul Khan, 29, a Birmingham man threatened with deportation.
But church leaders were criticised by the Government for their intervention. The then Home Secretary Douglas Hurd reminded MPs that the Church had not enjoyed the right to offer sanctuary since 1623.