The photo doesn't really show the markings well but I really don't think this is a false widow.
If you zoom in you can see that the head is brown at the sides with a dark central stripe/v-marking, tapering towards the abdomen (Steatoda nobilis has a more even coloured head). The abdomen has high, silvery sides, ending in a scalloped like effect on the top of the abdomen (S nobilis has a lower running, pale band, especially visible at the front of the abdomen). The pale marking in the centre of the abdomen looks more like a flare than a pentangle/shield, typical of S. nobilis.
This is our friend, the harmless missing sector orb weaver (Zygiella x-notata most likely), a very common spider around hour homes, mostly outside, but occasionaly inside too.
I'm aware of 2 Steatoda nobilis sightings in Aberdeen. But they would seem to be very sporadic, once you get farther from the S, SW & SE of England.
Steatoda grossa is much more widespread but relatively shy & little seen, mostly a few wandering males.
Steatoda bipuncta is pretty much all accross Great Britain, but this spider is rarely implicated in bites & considered harmless.
The British Arachnological Society has a recording scheme, you can see maps (by species) of the UK via their site. Travel & commerce will no doubt see them spread eventually, however it's really nothing to be alarmed about...many of the reports in the papers pertain to areas where this spiders have gone unnoticed for many years...people are just spotting more of them because of the publicity, not because they are rampaging accross the country. They are docile & the bites might be uncomfortable, but not dangerous to healthy humans. Any bite/sting/cut/graze can become infected, this would seem to be the issue in the more dramatic stories...some stories in the press even revolve around harmless spiders mistaken for false widows (like your Z. x-notata) & subsequent, needless panic.
They are just everywhere in my region...it's business as usual, even here bites are pretty much unheard of. I have 2 S. nobilis living full time in my front room (I kick them out of the bedroom & bathroom though) & no doubt countless others (S. grossa & S. bipuncta) hiding away around my flat. There are much more present & tangible threats to my safety to be concerned with: traffic, lightning strikes, bees & wasps, fatty foods, herds of cows, falling fridges...you get the idea? ;-)