The three lions had a slow start to the match, but two goals by Cole, who came on at half-time, was the difference between the two sides.
But England failed to impress in the match and Capello need to get more out of his team if they are going to beat Croatia on Wednesday.
Andorra: Koldo, Ayala, Txema, Sonejee, Antoni Lima, Ildefons Lima, Pujol (Vales, 90), Vieira, Silva (Toscano, 66), Jimenez, Andorra.
England: James, Johnson, Lescott, Terry, Ashley Cole, Walcott, Barry, Lampard, Downing (J. Cole, 46), Rooney, Defoe (Heskey, 46).
GOALS
0-2 England (Joe Cole, 55)
0-1 England (Joe Cole, 46)