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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.

Police cars, ambulances and fire engines were involved in at least 3,636 crashes between April 2011 and March 2016.
North Wales Police recorded the most incidents of those who responded, but the majority involved minor damage.
The Welsh Ambulance Service said a crash on a 999 call could be "catastrophic".
North Wales Police 1,506
Welsh Ambulance Service 735
Dyfed-Powys Police 567
South Wales fire 313
North Wales fire 280
Mid and West Wales fire 235
Figures obtained under the Freedom of Information Act showed North Wales Police officers were involved in 331 collisions in 2015-16 - down from 361 the previous year.
The force was criticised last April when officers used a police car to deliberately run over and kill a dog which was loose on the A55 in Conwy.
It reportedly cost the force Â£1,561.48 to repair the car involved but it said the majority of its reported collisions in the past five years were for minor damage.
Stephen Roberts, North Wales Police's head of facilities and fleet department, said: "The majority of North Wales Police vehicles are in constant use, responding swiftly and effectively to challenging and emergency situations. Our fleet of 557 vehicles cover vast distances in all weather and road conditions.
"For the period in question all incidents were reported. This includes minor scrapes or damage to vehicles which accounted for 74% of incidents during 2015.
"Prior to 2015, we did not distinguish between collisions and minor damage."
The Welsh Ambulance Service recorded the second highest number of incidents - 150 of which happened while on an emergency call.
Incidents since April included a driver who died following a crash between two ambulances on the A499 in Gwynedd.
Andrew Challenger, head of driver trainer at Welsh Ambulance Service, said emergency drivers were trained to anticipate risks and respond to hazards on the road.
He said people often panicked when they saw emergency vehicles, but urged them to stay calm and advised them to find a safe place to pull in to allow them to pass.
Dyfed-Powys Police, which provided information from 2012 to 2015 only, said 75 of its crashes happened while officers were attending emergency calls.
A total of 26 people were injured in collisions involving the force's vehicles, including 19 officers.
Gwent Police and South Wales Police would not provide figures.
Among the collisions involving fire service vehicles was a crash between and car and a fire engine in Swansea in 2013.
Of the crashes recorded by South Wales Fire and Rescue Service, 156 happened on emergency call-outs.
Mid and West Wales Fire and Rescue said its incidents were a mix of attending or returning from incidents, routine activities or damage found during vehicle checks.

The Fringe act Dolls, who work with the Cirk La Putyka, carried out the stunt above traffic on Friday.
Josa Koelbel and Bellina Sorensson, from the Czech Republic, dangled from the bridge in a bid to promote their show at the Underbelly Lafayette tent.
Edinburgh City Council said the performers had failed to apply for a licence.
An Edinburgh city council spokeswoman said: "The council was not made aware of this performance which was not permitted or authorised."
A Police Scotland spokesman said: "Any artistic performance, event or demonstration where public safety considerations are required must obtain an appropriate licence from the City of Edinburgh Council.
"Failure to obtain the necessary licence may result in a joint inquiry by the police and council licensing board into the matter."
The circus was not available for comment.
People with heart problems in the West Country could be at risk because of longer waiting times, the BBC understands.
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There have been more than 3,500 crashes involving emergency service vehicles in the past five years.
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A police investigation has been launched into a Fringe trapeze stunt from an Edinburgh city centre bridge.