Virginia Hernández and Quico Iñesta packed their suitcases in 2011, as they stood on the threshold of their 30s. "Ours was a double brain drain," she said over the phone. They left behind family and friends, and a decade of education at publicly funded Spanish universities; with them, they took their knowledge, which they now apply in the rainy city of Dundee, on the east coast of Scotland.

The doctor and her husband, a biologist, had been among the almost 1 million graduates swelling the ranks of Spain's unemployed, in country that produces an above-average number of graduates (40% of 25- to 34-year-olds against the European Union average of 34%). There is no official figure for how many of those have left since the crisis began, but various estimates put the number at about 300,000. These are the human face of the "unprecedented flight of talent" to which the employment minister, Fátima Báñez, has referred.

For Hernández, what hurts is the weather. That, and the waste. "It makes no sense to educate us for 11 years and then be unable to offer us anything afterwards," she said. Job security in Scotland and the earnings – £48,000 for her, £32,000 for him – compensate, in part, for the homesickness.

On the Spanish side of the water, the debate goes on. José Luis Alvarez-Sala, dean of medicine at the Universidad Complutense in Madrid, is clear: "We are producing more doctors than we can absorb." And every year, about 7,000 more qualify in one or other of Spain's 39 universities of medicine. To train a specialist takes between €60,000 (£48,000) and €70,000. But according to the dean, one in four of those graduates leaves the country to look for work.

"We need to rethink our teaching strategy," he said, "and quantify the real need for specialists." The brain drain, which affects mainly technical careers, has one peculiar aspect in the field of health: at the same time as specialists are leaving, gaps are being filled by professionals from outside the country. "Many recently qualified foreign doctors come here to specialise, and end up staying," Alvarez-Sala added.

Something similar is happening in nursing. With about 250,000 professionals, Spain suffers from a shortage in the workforce in every one of its regions, according to the country's general council of nursing. Spanish hospitals employed nearly 12,000 foreigners between 2003 and 2007, mainly in the private sector, in which Spaniards see fewer chances of getting an apprenticeship. Meanwhile, 6,000 nurses have left since 2002 in search of job security.

Raúl Muñoz, in charge of a human resources business in Frankfurt and himself the son of Spanish migrants, said: "They are very sought-after because of their good training and because of the transferability of their qualifications." He has just picked 40 candidates from Madrid, who will move to Frankfurt in the summer after completing an intensive course in German. Some will be back in five years' time, Muñoz said; others will stay abroad permanently.

Hernández said she would love to come home soon. But she is pregnant, and she fears that no clinic in Spain would offer her work, not even on a daily basis as a locum; in Scotland, they have guaranteed her a year's maternity leave and a renewal of her contract.