O2, the exclusive carrier for Apple's iPhone in the UK, reports that the iPhone 3GS is currently "out of stock".
In a statement on its website it says "Due to the phenomenal demand for the new iPhone 3GS, we've temporarily run out of stock online, over the phone and in our retail stores.
"We expect additional stock of the new iPhone 3G S to be available online, over the phone and in our retail stores at the end of this week.
"Please continue to check o2.co.uk/iphone for updates."
O2 states that the iPhone 3G 8GB is still available in all channels.
Apple's US retail stores reported shortages of some models of the new iPhone 3GS on Sunday, according to the company's own inventory tracking tool.
The shortages were a milder repeat of last summer, when Apple's stores quickly exhausted supplies of the then-new iPhone 3G, a situation that persisted for several weeks until the company could refill the pipeline.
On Sunday, Apple's stock-checking tool indicated that 13 of the 211 stores in the US, or 6% of the total, were completely out of the iPhone 3GS.
Another 31 stores, or 15 per cent, had only one of the four models for sale.
Apple revealed that it sold more than a million iPhone 3G S handsets over the first weekend of sales, despite the high cost of upgrading from previous models of the smartphone.
The figure exceeds that predicted by Piper Jaffray analyst Gene Munster, who thought 500,000 handsets would be sold.