Carphone Warehouse is now out of stock of 16GB iPhones, following the fast sell-out of 8GB models of the device last week.
Both Carphone Warehouse and O2 have also sold out of the 8GB iPhone, following their application of a £100 discount on the device last month.
Speaking to The Guardian, the companies also confirmed they will not be re-stocking their shelves ahead of the launch of the new version of the device over the summer.
“Apple is believed to have stopped making the basic version of the iPhone while it puts the finishing touches to a new 3G version which could be unveiled at its Worldwide Developers' Conference in San Francisco in June,” the report adds.
UK sales are thought to have exceeded those in either Germany or France, with several hundred thousand sold.