The programme allows people with unofficial or counterfeit USB charger to swap it at an Apple store for an official adaptor at half price.
Apple customers in the UK will be able to swap any charger they are unsure of from August 16th (Friday).
Normally the official USB charger costs £15. Under the take back programme, Apple will be offering an official replacement for £8.
It is also necessary to take your iPhone, iPad or iPod Touch with you to prove you own one.
Japan, Germany, Australia, Canada and France are the other countries the take back programme is being extended to on August 16th.
The death prompted calls for Apple to do more to deal with the problem of counterfeit chargers available on the market.
Originally, the programme was restricted to China and the United States.
The programme will end on October 15th for all regions, including the UK.