But Samsung beats Apple sales in the US.
The iPhone 5S and 5C were the best selling smartphones in Britain in May, with Samsung's Galaxy S5 only reaching third place despite the month being the phone's first full sales period.
However, among new Galaxy S5 buyers in Europe, 17% switched allegiances from using an iPhone, although more than half of Galaxy S5 buyers were existing Samsung device owners.
The sales data comes from Kantar Worldpanel, which classes the big five European markets as UK, Germany, France, Italy and Spain.
Across these markets, Android managed to retain the title of top mobile operating system with a 73.3% share of the market. Apple came in second with a 16.6% share and Windows was third with a share of 8.1%.
The strategic insight director at Kantar Worldpanel, Dominic Sunnebo, said: "The Samsung Galaxy S5 has had some success in attracting former iPhone owners across Europe. In general, consumers buying the Galaxy S5 were primarily attracted by its large screen size. This is something Apple is likely to address with the rumoured larger screen iPhone 6 launch expected in late September.
"In the USA the Samsung Galaxy S5 was the second highest selling smartphone in May just behind the iPhone 5S. However, at a total brand level Samsung claimed the top spot with 36.8% of sales versus 32.5% for Apple over the past three months. Apple loyalty is high in the US, with former iPhone owners making up just 8% of Galaxy S5 sales. The majority of those switching to Samsung were LG and HTC users."
Worldwide, Samsung shipped 10 million Galaxy S5 smartphones in the first 25 days on the market, the Korea Economic Daily reported.
The newspaper did not cite where it got the figure, but the news is consistent with previous sales reports from Samsung. Samsung reported that it was seven months before the original Galaxy S sold 10 million units, and five months for the Galaxy S2.
Apple's iPhone 5S and 5C models, which were released in September 2013, sold a combined 9 million units in just three days.