Very difficult to say from the quality of the shot & lack of scale. How big do you estimate the body size & leg span to be? What did it do when you turned the light on?
When I blow the image up there appear to be lateral stripe like markings on the abdomen? Google "Meta menardi"...?
I would say the spider is the size of a 50p. When the light was on it, it didn't really move.
Better photo go to:
About the size of a 50p, including legspan? The Twitter photo looks much more like a Steatoda grossa, a native false widow species. I have them around my home but rarely see them. I wouldn't be concerned. Possibly relocate any wandering males you might find, but they are quite reclusive.
A cave spider (Meta menardi) can grow much bigger and is more inclined to shuffle off out of the light to a hiding place.