Roger King and Edward Cook had attacked as 'unreasonable' licensing conditions laid down by Lincoln City Council that all licensed taxis must be wheelchair-accessible.
But Mr Justice Ognall refused to open the way for a full judicial review of their case.
The taxi drivers had failed to exhaust the 'alternative remedy' of appealing against the convictions to the magistrates court, said the judge, adding that it would not be appropriate for the High Court to intervene.
Counsel for Mr King and Mr Cook, Paul Epstein, had told the court that the case raised 'matters of considerable importance' for many Lincoln taxi drivers.
Since the wheelchair-access policy came into effect in April this year the numbers of taxis in the city had been greatly reduced due to the problems of adapting to the new regime, he told the court.
Numerous other would-be applicants were anxiously awaiting the outcome of his client's case.
In January 1991 the city's taxi drivers were told that the council's transportation committee had recommended that in future all Hackney Carriages would have to provide access to wheelchairs.
The costs of converting a conventional taxi to meet the needs of the disabled can be heavy and many taxi drivers immediately objected, said Mr Epstein.
But early this year the council resolved that from April 'Lincoln City Council will only permit vehicles that are wheelchair-accessible to use the public ranks and apply for a permit to use the British Rail forecourt rank'.
On March 29 this year Mr King had his application for renewal of his license refused because of lack of wheelchair-access to his vehicle. Mr Cook suffered the same fate on April 20.
Both claimed that although the wheelchair-access requirement might be appropriate to a large city like London they were not so for smaller communities.
The condition was also alleged to be illegal under European Community law free-trade principles.
Mr Justice Ognall declined to rule on the rights or wrongs of the taxi drivers' complaints. The court heard both men now have appeals pending before local magistrates.