The vacuum cleaner tycoon wanted to place the college at the old Stothert and Pitt crane plant site.
The 61-year-old had pledged £12.5m towards the project which was to be jointly funded by the government.
Sir James said the government had now rejected his latest funding proposal. "We have no choice but to abandon the plans for the school," he added.
The school, which would have pioneered new ways of teaching design and engineering, had been hampered by four years of planning and funding battles.
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