Mundella was born in Leicester, Leicestershire, England in 1825. Mundella was the first of five children of Antonio Mondelli (later known as Anthony Mundella), a refugee from Lombardy of uncertain background, and his wife Rebecca Allsopp of Leicester. At the time of Mundella's birth, his father was a poorly-paid trimmer in the hosiery trade (but he later became a successful cotton and wool waste merchant). His mother made lace on a lace frame in their home and was regarded as adept at this work but, nonetheless, she too was poorly paid and after rent for housing and for the lace frame there was invariably little left to live on.