This is a male garden spider (Araneus diadematus), a very common spider in the UK. Do you have a lot of foliage around your bathroom window(s)? He'll be perfectly happy if you relocate him outside onto some bushes, they also sometimes set up home on window frames. They can look a little gruesome but aren't aggressive, though they can bite if severely provoked, normally being quite docile. They are pretty difficult to catch & contain too, so sometimes it's easiest to make a path for them to escape & shoo them back outside, gently encouraging them with a sheet of paper etc. They will normally turn & run, rather than try & resist.
I have several that have made their way indoors, from plants in close proximity to my living room windows, they really aren't a problem & I see no reason to forcibly remove them. But maybe trimming back any foliage close to your bathroom window may reduce the chances of them wandering in again, in the future?
Yes, you are correct in that we have a heck of a lot of Wisteria covering the back of the house around the windows. In fact, my Son has some growing in through his bedroom window and has great joy in pretending that it is a Triffid! He likes spiders, though, so the threat of more spiders coming in won't persuade him to cut the offending tendrils off! My other half despairs.
We've plenty of other spiders in and around the house (probably due to the wonderful Summer weather we are having) and this particular one stood out due to it's striped and angled legs. We have watched him today and he exhibits a 'hanging around' demeanour from the ceiling (approx 6 inches or so) with his legs spread out as if in wait to catch a passing fly. Most amusing to watch. I'm sure he'll have more luck outside, that will please my other half! I'm not showing her your reply or she'll have me hanging off a ladder with some shears before the day is out!!