The Medicines and Healthcare products Regulatory Agency (MHRA) are aware of no instance of a patient having their implanted heart device interfered with by a high-voltage power line. MHRA operate systems where patients and cardiologists are encouraged to report instances of device interference or malfunction from any source voluntarily to MHRA (the "yellow card" system that is available for all medicines and devices as well as specific systems for implanted medical devices). Heart device manufacturers are required by law to report incidents to MHRA which represent actual or potential serious injury to patients. It is therefore likely that if such instances did occur, MHRA would have heard about them, but this cannot be guaranteed.
Note: MHRA do not currently discuss power lines on their website at all, although they do discuss several other source of possible interference. This in itself indicates that MHRA do not regard power lines as a significant risk to implanted devices,
National Grid, which operates the high-voltage electricity network in England and Wales, runs a helpline for the public to report concerns about power lines, and is aware of no instances of interference with correctly fitted modern devices.
In addition, National Grid and other electricity companies have staff with implanted heart devices, some of whom are occupationally exposed to rather higher fields than can be experienced by the public underneath power lines, for example in substations, again with no instances of interference.
A similar experience of the absence of instances of interference, even on staff experiencing higher fields, is also reported by other countries such as France.
USA: Food and Drugs Administration
In the USA, there is also a legal duty to report device malfunction. The Food and Drugs Administration administer it and the resulting database MAUDE is available online. It is a massive database because it covers all possible medical devices, but we are told by colleagues who have searched it closely that there are no confirmed instances of interference from transmission-line EMFs.
Thus there is considerable confidence in saying that based on the absence of reported incidents, power lines do not appear to interfere with implanted heart devices.
This is broadly consistent with the level of immunity from interference required by the standards that implanted devices are designed to.