Eight days after O2 and Carphone Warehouse, Apple’s U.K. distributors, tried to rid themselves of unsold iPhones by instituting a 100 pound (37%) price cut on the 8GB model, the extra phones have all but disappeared.

On Thursday, Carphone, Europe’s largest independent mobile phone retailer, alerted advertisers that the sale had done its work: the 8GB models were gone and would probably not be replaced. Pocket-lint, a British gadget site, posted a copy of the message:

“Thanks to the most phenomenal response to the promotion, The Carphone Warehouse is now out of stock on the Apple iPhone. Please can you remove all reference to the iPhone promotion in your copy. We apologise for the short notice but would like to thank everyone who participated in the campaign. Carphone do not expect to receive any additional stock at this time.” (link)

The news follows a week of intense activity at both Carphone and O2 stores. According to a report last week in Britain’s Mobile Today, sales at Carphone’s flagship store on London’s Oxford Street had doubled from 30 per day to 60 after the promotion was announced. “We usually sell one or two a day,” one staffer told the website, “but yesterday we sold about 20 – it was like launch day again.” (link)

8GB iPhones were also sold out last week at O2 stores in Newcastle, Birmingham and London, but O2, the British arm of Spain’s Telefónica, hopes to replenish its supply. The 16GB model is selling for full price and is still in stock.

The price cuts were part of a global effort to clear inventory of first-generation iPhones in advance of the so-called 3G iPhone, widely expected to be announced in June — perhaps as early as June 9, according to a CitiBank report issued on Thursday.

Although Apple (AAPL) has been having trouble meeting demand for iPhones in its U.S. stores, sales have been sluggish in Europe. The reaction to the O2 and Carphone promotion suggest that it was price, not lack of 3G connectivity, that was hampering sales — at least in the United Kingdom.

In France, where iPhones have not yet been marked down, it costs 399 euros to buy an 8GB model (VAT included), or $626. As Silicon Alley Insider points out, it’s cheaper to ask a friend to pick one up on vacation in the United States, where the same phone sells for for $399, and unlock it.

It’s not clear what’s going on in Germany, where T-Mobile slashed 8GB iPhone prices 75% to 99 euros ($155), but it still seems to have plenty in stock.