I've encountered several of these spiders in my attic, there seems to be an awful lot of dead wodlouse scattered in one area of the attic where I've found 3 of these spiders, when I've moved bags around in the attic.
This is an adult female Steatoda grossa - so yes one of our False Widow species. They usually make their webs within a foot or two of the ground, but this will include the floor of loft spaces etc. T this species is not reliably implicated in bites and as she is doing such a great job if keeping the Woodlouse population down (and they will feed on damp timbers) I would leave them be.
For more info. about False Widow spiders please see the following links:
Thank you for your quick response on the identification of this spider, I have allergies to bee and wasp stings and where I've found these spiders in my attic, they are sited around the attic hatch, I don't wish to be on the receiving end of a bite if they are disturbed gaining access to items which are stored in the attic.