Illum was born on 5 July 1863 in Dyvskrog at Fåborg on the island of Funen, the son of ship builder Peter Hansen Pedersen (I.)

Illum was apprenticed to V. Wegener in his new home town and then worked for a few years at Frølund & Wittrup in Horsens.

His business grew rapidly, assisted by substantial credits from his old employer, which compensated for his very small initial capital.

In 1899, he had grown out of space and moved his business to larger premises on the other side of the street and would continue to expand into successive properties over the following years.

[1] In 1913, Illum established a pension scheme for his employees which became a model for similar initiatives in other large enterprises.