Thanks guys. After doing some more reading last night I've decided to try the Zap-a-Gap glue. The Zap glue has a much lower viscosity than the JB Weld which I'm hoping will make it easier to flow into the gap.
I picked some up this afternoon and will have a go at repairing over the weekend. Unfortunately I don't think I'll be able to separate the parts, the hinge pin looks like it's plastic and without the proper tools I don't want to risk damaging the pin or hinge further. This particular Zap glue is supposed to be about the consistency of maple syrup and I have a few millimetres of clearance so with care I should be able to keep it from getting everywhere.
Will let you know how it goes.
