Almudevar was born in London, England on 28 June 1978, to a Spanish father and a British mother. She grew up in Nottingham. Almudevar graduated from the University of Leeds in 1999 with a degree in European Studies. She wrote for the university newspaper, the Leeds Student, while attending the school.
Almudevar moved to Brussels, Belgium, following her graduation, where she worked for the European Union. She was subsequently awarded the Heinz-Schwarzkopf Foundation's Young European of the Year prize in 1999 for her work in promoting unity among diverse young people through her journalism.
She was first hired by the BBC in 2002. She initially worked for BBC Midlands. Almudevar also worked on radio and television programs while working at BBC Midlands, including Midlands Today and Inside Out. She also created "docu-dramas" for the network before becoming an overseas reporter and correspondent for the BBC.
According to BBC News, Almudevar won an award for her work on Alexandra Road, a ten-part series that followed the lives of residents of a street in Wolverhampton, United Kingdom, which she co-produced with fellow BBC journalist, Brady Haran.
She took a sabbatical leave from the BBC in 2006, when she travelled to several Latin American countries, including Bolivia, Colombia, Peru and Argentina. She produced a number of news pieces while on sabbatical which focused on issues facing the region, including street children and a campaign to legalize the production of the coca leaf.
Almudevar and other journalists had been traveling to the Bolivian city of Sucre to cover political unrest in the city due to the approval of a new regional draft constitution. Flights had been suspended to Sucre so Almudevar had been forced to drive instead.
Almudevar's taxi reportedly crashed head on into two stopped trucks which had been involved in an earlier accident. Lola Almudevar was killed in the accident, along with two of the truck drivers, as well as Clotilde Fernandez, the wife of Almudevar's taxi driver. Spanish Reuters reporter Eduardo Garcia, who was traveling with Almudevar to Sucre, was also seriously injured in the accident.