Around 60,000 motorists were hit with penalty notices after crossing Lendal Bridge in the city, after controversial traffic calming measures were introduced last year.
The Council, which defended the restrictions as necessary to resolve traffic issues in the area, is now deciding on a process through which motorists can claim back money paid in fines.
Councillor David Levene said: "Whilst the trial achieved some of its aims, it had become too polarising an issue, requiring too much resource, and so detracting from other necessary transport policies," reported the Daily Mail.
He went on to say that refunds would not be volunteered and that motorists would have to apply for them:
"An application will have to be made for refunds to be given as 'a statement of goodwill' and will not be volunteered as that would legally say the scheme was wrong."
The debacle has led to call for the Council's leader to resign. Cllr Keith Aspden, leader of York's Liberal Democrats, told the Daily Mail: "The closure of Lendal Bridge was botched from start to finish and has done deep reputational damage to York," referring to the large proportion of tourists who were subject to penalties, making up around 80 per cent of those fined.