One of my theories that I will be using for my English exam (on Friday) is that the Inspector is like Moses and the Birling family being like the pharaoh. The pharaoh in the bible decides to free the slaves and then doesn't and then God punishes him. In the book Mr and Mrs Birling originally doesn't accept any blame for what they did to "Eva Smith" but then the Inspector changes their minds. But soon after the inspector was exposed as being 'not a real inspector' they revert to their old mindset (except Eric and Sheila) just like the pharaoh does.
I believe in the introduction of the play it briefly mentions the seven deadly sins and below is who I believe the each sin represents.
7 deadly sins and possible character representations:
Gluttony (Mr Birling/Gerald/Mrs Birling)
Greed (Birling/Gerald/Mrs Birling)
Sloth (Eric? I dont fully understand the definition of sloth)
Pride (Gerald/Mr Birling/Mrs Birling)