No, it's not a false widow. It's a male lace weaver (likely Amaurobius similis, or fenestralis). A common spider around & sometimes in our homes.
I have read these can bite and cause swelling ...is that true
They are one of the dozen, or so UK spiders that can deliver a bite to a human. But this would be an extremely rare occurence, and no spiders native to this country are dangerous to healthy humans, as with any bite/sting/cut, signs of infection should be treated immediately. I see more brown lace weavers in my house than any other genus of spider, have even woken up with one crawling on me, without being bitten.
Throw any that you find outside, they're usually easy to catch. I use a cut down pop bottle, with the lid on, as a scoop. If they bother you, don't discourage the "daddy long legs" spiders (Pholcus phalangioides) as these love to eat Amaurobius species.