The Hammersmith and Fulham Community Law Centre claims the Tory-run council decided to reduce its grant by more than 60 per cent because the centre takes on cases some council members might oppose on ideological grounds.
However, the council denies the allegations, saying legal and welfare advice services receive a large proportion of its grant funding.
The law centre, which is a registered charity, learned at the beginning of April that its grant would be reduced by £160,000 as part of an overhaul of the council's voluntary and community sector grants programme.
"A couple of council representatives sit on our management council, and on a number of occasions they have queried why we sue the council when we are being funded by it," said Toufique Hossain, an immigration solicitor at the centre.
"They also said they weren't happy with us dealing with certain cases or legal areas."
Last year, for example, the centre represented nine Afghan aeroplane hijackers who challenged a Home Office decision not to allow them to stay in Britain.
"It got a lot of publicity but was funded wholly by legal aid and had nothing to do with council funding," said Hossain.
Hossain said the council, which is led by Conservative Stephen Greenhalgh, has also withdrawn all its funding to the Horn of Africa Community Centre, which supports north-eastern Africans living in the borough.
The council told voluntary groups it was reviewing its grants programme in order to accommodate its funding priorities for the next four years.
It said it would redistribute grants to groups that would help it build safer and healthier communities, support the elderly, children and young people, promote economic development and provide value for money.
But George Sheerin, chair of the law centre's management committee, said: "Our funding application fits with council priorities and is the result of 27 years of partnership with the council and other local advice agencies. This is not a rational decision. There is a political agenda at work."
Antony Lillis, Hammersmith and Fulham's cabinet member for community services, denied any discrimination against the centre.
"The law centre is among a number of legal and welfare advice services the council is funding," he said.
"Welfare and legal advice groups account for 12.5 per cent of the overall grants budget, which is exceeded only by organisations supporting older people and children."