People are failing to attend hospital appointments on time after a change in concessionary bus fares.
The alarm was sounded by Goring councillor Peter Welch at a meeting of Worthing Borough Council's executive.
Coun Welch said many elderly people trying to get into town before 10am had to pay full fare, yet the number eight bus serving his constituency usually had no more than two or three people on it.
Previously, the concessions came into force at 9am.
He said: "The bus companies should be approached by the council and told to reconsider the time limit."
However, council leader Sheila Player said: "As soon as we realised the change was going to be made to the concessionary fare regime we made strong representations to Stagecoach saying they should rescind their decision and they refused.
"They are quite separate from this council and are allowed to determine their own fares, which is most unfortunate."
Meanwhile, the council has extended its bus pass scheme to allow free off-peak travel to registered blind and partially-sighted residents.
Coun Player said: "Representatives of blind and partially-sighted residents asked us to issue special passes which would enable them to travel entirely free during off-peak periods.
"We thought this was an excellent idea and agreed to it after discovering it could be done inexpensively and from existing resources.
"The special passes, which are red, to alert bus drivers, will save these particularly disadvantaged residents from having to handle money while trying to negotiate their way on to buses.
"Free passes can also be issued to the nominated companions who accompany these passengers."
The passes are being issued to new applicants immediately and will automatically be offered to existing customers when their passes are due for renewal.
About 9,500 pensioners and disabled residents in Worthing hold Countycard bus passes with which they can travel on most bus services in Sussex, at half fare, during off-peak periods.
Worthing's concessionary fares scheme will cost approximately £278,670 this year.
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