As someone with both a degree in biology which included entomology and working in various fruit packing factories, you'd be very wrong to say that exotic insects very rarely make it to the UK. Very.
I found a hairy, hand size tarantula on a pineapple alive. I'm not just being a pathetic screamer. I know what it was because I I'm sure I know more than someone who has not studied entomology to my level.
Various scorpions running off into the Kent County side. Black widows daily in grapes to m&s. We found 20 in one day. Snakes. They all survive cold store very nicely. One day in Fyffes someone was bitten in the face by a massive spider getting a box of bannanas off a pallet.
How they fair out in the open I don't know. Dispite all of this I don't know anyone who was bitten personally so it was still very safe.
Anyway it looks to me like a tunnel / funnel type spider but it's really hard to tell on my phone. Size of Web is not related to spider size. They just lerk in the nests, unlike spiders inside that love to run about. I could pick any insect up outside, I still dislike them in the house. Just because I dislike them, doesn't mean I'd ever kill one.
Did the op say she wanted to kill it? I think not.