Yes it is a false widow Steatoda nobilis. Got several here out the back of the house, around the shed and in the conservatory too but they keep themselves to themselves and dash for cover at the slightest hint of disturbance. Unless they're dealing with prey caught in the web by day (usually an unfortunate bumble bee) they only really emerge on to the web at night. A female will tend to stick to the same spot unless forced out - we've got one that's been living in the same gap by a window frame for over a year. Males wander more but I've yet to notice one indoors here - but like you I'd be inclined to show it the door.