OP,
Definitely nothing to worry about with the spiders. I assume you are in the UK? We have no dangerous species of spider here. Technically they're all venomous but they are totally incapable of harming a human as the toxin is milder than a fairies fart.
Good analogy with the terrorist attacks, I quite like that one!
With the giant house spider, I hear this quite a lot (I'm a bit of a spider guy) escorting them off the premises, unless you put them into alternative accommodation means they will perish very quickly. House spiders (including the giant) have evolved to live indoors and can't survive outdoors. Of course it's up to you if you can or can't tolerate them being in your house, but again they are completely harmless.
Sometimes people say "I try not to kill the house spiders, I just put them back outside" - thing is, you can't put something "back" outside that was never outside in the first place.
My best advice is to just wave as they pass by, you only really see them in the autumn, the rest of the year they're just doing spidery stuff where you can't see them. They appear in autumn to mate, 90% of the ones you'll see are the males on the hunt for some saucy spidery action!
If you find them in the bath/sink/wash basin they are in there for one of two reasons, either they saw a droplet of water (spiders do drink water) or they just wandered in and can't get back out. Leave a bit of bog roll hanging over the side of the bath and come back in half an hour - spider will most of the time be gone.
Not trying to convert you or any readers to liking spiders, just saying they can't hurt you and there are actually many benefits to letting them get on with their autumnal blasting around :)