Cases of lost or stolen passports and travel documents reached 28,783 in 2012/13 - a slight rise on the 28,659 in 2011/12.
Spain, with more than three-quarters of a million British residents, was the country with the most requests for consular assistance at 4,658, down from 5,405 the previous year. It was followed by the USA and France.
But the FCO said there had been a "significant decrease in arrests and hospital admissions.
It said alcohol "continues to be a major factor" in cases involving young people in the Balearic Islands, Turkey and the Greek islands.