The far right’s 10-year grip on Denmark’s government has ended as the Danes voted for their first female prime minister, handing government to a centre-left coalition.

The close general election gave victory to the social democrats, closing a decade of rightwing ascendancy during which a minority government of liberals and conservatives was kept in power by parliamentary support from the europhobic, Muslim-baiting Danish People’s party.

Helle Thorning-Schmidt, the social democrat leader and daughter-in-law of Neil and Glenys Kinnock, salvaged her political career by ousting the liberal prime minister Lars Lokke Rasmussen’s coalition at her second attempt. She is expected to form a government with two other centre-left parties.

Her victory, though, was narrower than predicted and could produce a fragile coalition. Her “red bloc” secured only a three-seat majority of the 175 at stake in mainland Denmark, with almost all votes counted. A further four seats reserved for faraway Greenland and the Faroe Islands had still to be declared. The expectation was that the centre-left would emerge with a five-seat margin in the 179-seat chamber in Copenhagen.