Mr Justice Popplewell, in the High Court, granted them leave to bring a judicial review of a decision in June by Greenwich council not to use its powers under the 1984 Road Traffic Regulations Act to close roads when they are a danger to health.
However, the judge warned the families not to anticipate victory. He said the case was "just about capable of being argued and should be argued".
The hearing should take place before Christmas.
Graham Read, for the families, said there was overwhelming evidence that air pollution, especially from car emissions, had an effect on asthma sufferers.
An expert report indicated that Trafalgar Road, Greenwich, south-east London, was particularly subject to problems because it was in a valley and because of the density and proximity of housing.
There had been insufficient consideration of the evidence by the council because it had misunderstood the scope of its power under the Act.Reuse content