It doesn't strike me as obviously being a false widow (I have 2 false widows within arm's reach right now). How big is your spider, body length without legs?
Lots of spiders hang upside down, like sheet web spiders, try googling "linyphia triangularis" for instance?
Even if it were a false widow & outside, there is little chance of you coming into contact. I have them indoors & mostly see the same one over & over, sometimes 1 or 2 others appear from time to time over the course of a year, but there must be many more than that around me. They are pretty shy and avoid contact with people whenever they can. No false widows are dangerous, there are even false widow species that are totally harmless.
Where I live, false widows are a daily part of life & in/around most people's homes, offices, cars, sheds...though few people are aware that they are so common.
The papers like to blow them out of proportion every now & then, there seems to be some scaremongering going on right now, remember the "false" bit, they are not black widows.
I know what it is to hate spiders, I was absolutely petrified of them for the first 42 years of my life! Since moving into a place where I simply can't avoid them, they just don't bother me any more.
Thank you for putting my mind at ease, it is definitely Linyphia triangularis, the big money spider, now I feel silly.
I'm not normally one to take notice of the scaremongering, but if it involves spiders or ants I will always believe the worse no matter how Ludicrous it is.