Yes, the photo shows Steatoda nobilis, the so-called 'noble false widow', the spider which the media make such an unjustified fuss about. It has been frequent in the southern coastal counties of England for a great many years, and is nowadays frequent and abundant in many areas of southern England and Wales, including the south coast, south-west, south-east, London area and East Anglia, and increasingly much further north. The media frenzy caused by this spider is unwarranted. Steatoda nobilis spiders are unobtrusive, have no interest in attacking humans and would only bite if they were put into a position where they do so as a defensive reaction. Honey bees and social wasps pose a far greater risk. There are a number of other 'false widows' in Britain, some which are native or have been in the country for centuries, so there is a lot of misinformation about these spiders. They are probably widespread in your whole local region, so there would not be much point in trying to remove them, and you simply need to not deliberately pick them up or squeeze them etc.
You can see some sensible information about false widow spiders e.g. on this website, the BAS website
and Buglife website.
