Just three teams of the 20 that started are still flying in the Gordon Bennett 2010 international gas balloon race.
In third place are Wiltshire adventurer David Hempleman-Adams and Simon Carey, who had travelled 1,944km (1,208 miles) by 0628 BST.
A German and US team, in second and fifth place respectively, are also in the air.
The teams, which launched near Bristol on Saturday, are aiming to fly the furthest.
Germans Wilhelm Eimers and Ullrich Seel, currently in second place, had travelled 2,192km (1,362 miles) by 0629 BST and were flying over Romania.
US team Richard Abruzzo and Carol Rymer Davis, the third team flying, had travelled 1,751.90 km (1,089 miles) by 0628 BST and were over the Adriatic Sea.
Mr Hempleman-Adams, from Wiltshire, posted on the team's blog at 0544 BST: "It's been the coldest night with the low point being when some of the ballast froze in the bags.
"It was about minus 1 degree Celsius (or 30 degrees Fahrenheit). So we've been shivering on and off. Our speed has been up and down and direction left and right.
"We've been on oxygen most of the night, mountainous terrain below.
"We're now south of Belgrade with rain ahead of us which I want to avoid. There's nothing quite like being frozen and rained on in a balloon basket."
Two British teams were forced to land on Monday.
Britain's Janet Folkes and Ann Rich descended in France after flying 1,037km (645 miles).
Colin Butter and Paul Spellward also came down in France after flying 916km (569 miles).
The balloons are controlled by releasing gas to descend and throwing out sand to ascend.
Switzerland's Kurt Frieden and Pascal Witpraechtigeis landed in Romania earlier in first place, having travelled 2,435km (1,513 miles).
French team Sebastien Rolland and Vincent Leys are in fourth place having landed in Italy, travelling 1,805km (1,122 miles).