Judging by the corrosion and the black soot marks on wiring on that last picture, really is not worth using or tampering with, much safer to replace that part at very least and as NickAu says, can be dangerous if you don't know much about this sort of thing.
Either replace the entire light fitting or you could do as Byron says, remove all the gubbins from in the light unit and buy some cheap hardware light fitting that will fit inside that, not particularly difficult to find or to do, just get as close to the same sort of hardware as what is on the light unit already and replace like for like.
Just depends on how you feel about either method being easiest and fits your budget.
Quailified electronic engineer or electrican will not do the job for you for free (unless you know of a mate who might do it for you), likely to charge £50 per hour at least or they may simply refuse to do the job as not worth it.