Kay Gannon, 22, surprised an intruder who cut her throat when she returned to her rented flat after visiting neighbours.
Her Spanish boyfriend, Manuel Farrona, returned home to find her dead in the bathroom and their baby lying on the floor crying, blood-stained but unharmed.
Ms Gannon, from Market Harborough, Leicestershire, went to Spain with her parents five years ago to start a new life.
About a year ago she moved out of the family flat, about five minutes away, to set up home with Mr Farrona, whom she met while working in the kitchen of his bar- restaurant.
Their rented flat was on the seventh floor of one of three apartment blocks in the centre of Calpe, where about 40 per cent are owned by Britons, most of them retired.
The police are following various leads, including a tip about someone seen 'acting unnaturally' as he ran to his car and drove off frantically.