Def Leppard was founded, like many bands in Sheffield at that time, in 1977.
By 1979 their success enabled them to quit their day jobs and focus on music. They outgrew Sheffield soon and become initially more successful in the USA than the UK. Their third album Pyromania finally gave them their big break worldwide and in the UK.

They were more part of the rock music scene in Sheffield and initially had more of a big following outside the UK, so they weren't around in Sheffield
when the music scene in Sheffield peaked in 1980.
Even still, there is an early connection between Joe Elliot and Stephen Singleton (Vice Versa/ABC), who were mates at primary school where they formed their own band. They went to different schools after that, so they went their own ways, both ending up in very successful bands
in totally different genres of music.

def leppard fan site