And it was Magnusdottir who shot Iceland into the lead with a low 18-yard shot in the 26th minute.
England's first on-target effort, a 43rd minute header by captain Faye White, was cleared off the line by right winger Dora Larusdottir.
Midfielders Emily Westwood and Jill Scott had long-range shots kept out by goalkeeper Thora Helgadottir in the early stages of the second half.
But in the 56th minute England's substitute keeper Carly Telford had to make a fingertip save from Vidarsdottir.
The home side's best effort arrived nine minutes later, striker Eni Aluko cutting across the penalty area to have a 15-yard shot well saved by Helgadottir.
England's hopes of saving the game were ended nine minutes from time, however, Vidarsdottir muscling her way through the middle to slide the ball past Telford.
Powell's team's final pre-Euro 2009 game is against Denmark at Swindon next Wednesday, 22 July.
She added: "Hopefully the players will bounce back and we'll head into the Euros on a positive note."
Iceland (4-2-3-1): Helgadottir; Sigurdardottir, Jonsdottir, G. Gunnarsdottir, O. Vidarsdottir; Gardarsdottir, Stefansdottir (Omarsdottir 70); Larusdottir, S. Gunnarsdottir, Magnusdottir; M. Vidarsdottir.
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