Can I get this done on the NHS?

Screening for conditions causing sudden cardiac death is not offered on the National Health Service if an individual does not have any symptoms or a family history of heart disease. In March 2005, the 8th National Health Service Framework Chapter in Cardiology was launched which was basically dedicated to arrhythmias and preventing sudden death in young people. This document suggests that screening should be offered to young individuals who have cardinal symptoms of cardiac diseases such as chest pain, breathlessness, blackouts without warnings; or those with a family history of inherited cardiac syndromes.
So in response to your question, if you don’t fit into that category, you will not be offered screening on the National Health Service. You would then have to go privately or to a charitable organisation that could make this possible at a very low cost, such as Cardiac Risk in the Young.