The photo isn't really sharp enough to make firm ID, but from the general shape & colouring, a male Steatoda nobilis can't be ruled out...but then, the males can be easily mistaken for other spiders unless inspected close up.
False widows aren't uncommon in many parts of the country, some species are more widespread than others. If you are confirmed as having S. nobilis (the one that grabs the headlines), then you're probably in a similar situation as many folk in the S & SE of England.
I have 2 in my living room right now & could no doubt find some S. grossa if I went on a hunt for them.
If the thought of them bothers you, scoop them up in a paper cone (fold over the tip, so they don't drop through, give it a quick shake so the drop to the bottom...they're good climbers) & deposit them outside. Be aware that they're not always easy to catch, so best attempted when the odds are in your favour & they're out in the open on a flat surface.
Males tend to wander more, looking for females. Females often set up home & stay in their web, close to a bolt hole.
They're typically not aggressive, bites (which are certainly not deadly, akin to wasp sting?) are often the result of them being crushed against the skin. Be aware that they are possibly around & excercise caution, evict any that trouble you indoors.