Researchers funded by the charity found that by looking at a specific group of genes they were able to reliably detect underlying problems.
It follows the death of Sir David Frost's son Miles, who died suddenly from a condition thought to have been inherited from his father.
His family aims to raise Â£1.5m to make genetic testing available in the UK.
The eldest son of the late presenter and broadcaster died last year, aged 31, when he was out jogging near his family's home in Oxfordshire.
He was suffering from an undiagnosed heart condition called hypertrophic cardiomyopathy.
Previous genetic tests looked at a small number of genes and were only able to identify specific conditions, leading to higher costs and longer diagnosis time - a major barrier to rolling the test out across the NHS.
But researchers from Imperial College London and the MRC Clinical Sciences Centre say the new test, which looks at 174 genes, is quicker and more reliable.
It has already been rolled out at the Royal Brompton and Harefield NHS Foundation Trust in London , with around 40 patients per month being successfully tested.
Dr James Ware, a consultant cardiologist specialising in inherited heart conditions, said: "Without a genetic test we often have to keep the whole family under regular surveillance for many years. This is hugely costly for both the families and the health system.
"By contrast, when a genetic test reveals the precise genetic abnormality causing the condition in one member of the family, it becomes simple to test other family members. Those who do not carry the faulty gene copy can be reassured and spared countless hospital visits."
The research has been funded by the British Heart Foundation and the findings published in the Journal of Cardiovascular Translational Research.
A new blood test could help diagnose people with inherited heart conditions, the British Heart Foundation has said.