It is one of 30 schemes throughout Britain, involving about 3,000 homes postponed by Persimmon, York's mega-housebuilder, until the uncertainty in the mortgage market blows over.
Building of the controversial flats, which were strongly opposed
Jeff Fairburn, Persimmon's northern divisional chief executive, said: "As soon the mortgage market frees up, particularly for first-time buyers, we will commit to the scheme.
"But the Barbican needs a big cash investment up front before you get a return. It is important to remember that there are affordable elements in this scheme to cater for first-time buyers and that will be affected by the economic slowdown."
He said that he did not believe the plans for a hotel on the site would be delayed as a result.
Meanwhile, Mr Fairburn announced that other huge Persimmon projects in York, such as the 700-home Germany Beck scheme in Fulford and the 175-apartment project called The Forum at Heworth Green, would continue.
He said Persimmon had yet to gain detailed planning consent at Germany Beck and ironing out the technical issues could take nine months. Complicating the issue was a separate application by residents to create a green.
"Hopefully, by the time we resolve the planning issues, the market will be back to normal," he said, adding that already half the housing project at The Forum had been sold and the other half, some of which were still being built, were being marketed still, in spite of a slowdown in response.
Persimmon, he said, was also committed to continuing with its £4.4 million 50-home project on the 3.2-acre site of the former Sundora fruit and nut factory in Burnby Lane, Pocklington. "We have started, so we'll finish," he said.
The move to shelve some projects was announced at Persimmon's annual meeting at York Racecourse yesterday shortly after the group became biggest faller on the stock exchange.
Shareholders were told the group's revenues were running 24 per cent lower this year after a deterioration in the market over the past three weeks.
Revenues for the year to date are about £1.37 billion compared with the £1.8 billion seen at this stage of 2007.
A statement issued by Persimmon welcomes the Government making available £50 billion to increase liquidity in the banking system to kick-start the mortgage market, but calls for extra action to help first-time buyers by increasing the threshold for stamp duty and further reducing interest rates.
"Because of the uncertainties of the global economy and the UK lending environment, it is difficult to predict when the market will improve.
"We are, therefore, focusing on management of cash flows within the business to ensure that our balance sheet strength is maintained. Close control of investments in work in progress, land, build costs and overheads are a priority for our experienced management teams. We are operating off five per cent more sites than a year ago. Against the backdrop we have postponed the start of scheduled new sites until the mortgage market improves."