A council spokesperson said funding was not available for the bridge project after costs rose twice.
A Studio E spokesperson said: "We are saddened that a project of such potential and international interest was killed for political reasons." The Millennium Commission, which urged the council to go ahead last month, has withdrawn £740,000 of funding for the scheme.
A commission spokesperson said it was disappointed with the decision and could not make any more funding available for the council's building programme.
Sources close to the scheme said the council would have to consider a bridge across the River Eden at some point because council policy committed it to providing a national pedestrian route and cycle route across the river.