Re: That's not a false widow.
It is a male false widow, the females have more bulbous abdomens, upto a max of about 50p piece size. House spiders (Tegenaria species, 3 in this country and difficult to tell apart without specialist knowledge and a microscope) are more hairy/less shiny and a variable grey colour (though again the males are less wide at the rear than the ladies).
We have loads of these lovelies in our car port. Despite me going out to take photos, for some inexplicable reason these vicious killers seem more inclined to run away from me than kill me. Very light sensitive too, especially the bigger ones. Get a torch on them and they scuttle back into their holes.