"In the US it seems to be common to sing from "The Book"'.
Not true Marje, only in certain circles where they can't get away from singing without a book! On the whole there are far more places in the US where singing from "the book" just doesn't happen.

"When in Rome do as the Romans"

It's been over 25 yrs since I've been to any music clubs/sessions overseas & that was only when I was in Ireland. I'm extremely excited to have been invited to perform at a festival in the UK in July & I'm dying to finally get to see & hear what your clubs & sessions are like. Not to worry, I make it a habit to see what's the norn before I embrass myself.

Here in the US we don't have the equalivent of your folk clubs in the UK or Ireland. We have club societies that run concerts & house concerts, bars & pubs that get used as venues & put on folk performers or have sessions but from your discriptions we don't really have folk clubs with regulars & their own floor singers where every so often hey put on "Guest" & have a few floor singers inbetween & after sets. There may be a few places that come somewhat close to that but it's not at all common.
However we do have some places were singers * musicians gather to play together & loads of sessions where there's hardly any singing, though as Tom mentioned above there are a few but they are not the norm buy any means. Then there are many Getaways, the best I've seen are the DC Getaway which many east coast muddcatters have been to & the West Coast's end of the yr Lark just north of San Francisco which I last attend almost 30 yrs ago but cna still taste.
Here in the US I do believe it's much more common for us to join
in.

When I perform, I do mostly worksongs & shanties. Songs that were meant to have others sing along with. I love people singing, I do care that they sing what I'm singing, tune & words but I want them to enjoy what they come out to do & that's sing, so when they're singing I'm happiest. If don't often sing ballads but I do love to sing them, I don't because mostly people want to sing. When I'm at an after hours "fringe" (sing session? not sure it's your word) at a festival & it's all singers pulling the "rare & uncommon" tricks out of their hats & it's just keeps getting better & better & the ballads are getting darker & longer, you can bet that a pin drop can be heard & that no one would brake the trance,,,,or sing along that's also true here.
It's different everywhere.
My opinion, first if you're the singer let everyone know straight out beforehand if you don't want them to sing or if you want them to join in, give them that respect & you will get it in return. If you're gonna sing a chorus song or something with a refrain here then expect that you'll get folks to sing along weither or not you ask. I always encourage folks to join & & if they sing the whole way through it their song to sing with I never owned it in the 1st place. I dont have much of a problem with others trying to lead me or sing over me or doing whatever they do, I have mostly found that before the song ahs gone to far they're right in set & in tune with me.
When I'm over there I'll do as you do but hopefully I'll be able to enjoy a song or 2 while I'm there

Captain Birdseye, I'll be looking forward to meeting up with you. I'm told that you're also on the bill at the Scarborough Seafest, yes??

Barry