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1 July 2015 Last updated at 11:08 BST
BBC West has discovered that four out of 10 patients are waiting more than 18 weeks, the government's national target, for treatment at the Bristol Heart Institute.
The BBC's Matthew Hill spoke to patient Balbir Kaur Nirwan, who had to wait six months before being treated, consultant Alan Bryan and Dr Kevin Fox, from the British Cardiovascular Society.
People with heart problems in the West Country could be at risk because of longer waiting times, the BBC understands.