I am putting this here as someone might be able to tell me, but if not hopefully techy will come along at tell me how to do it...
We have moved abroad and internet is not all that brilliant at times in our house, so I sometimes pop down the road to an internet cafe place and log in to mumsnet. When I do this I then have to log in on my home laptop each time I go back on that. Is there any way I can stay logged in to mumsnet on my laptop, but log in and out at the cafe?
Presumably you are logging out of MN on the internet cafe computer when you have finished your session (as you never, ever leave yourself logged into any site on a public computer!). That is logging you completely out of your account. That's why you're then logged out on your home computer as well.
No, a logout is a logout. Logging out of an account on one computer means that you are logged out of that account full stop.
I normally stay logged into MN, FB, my email and a couple of other sites. If I then use a different computer to access any of those accounts (when DZoH and I are sharing use of our notebook when we're on holiday for example) and log out on that computer I have to log back into all of those accounts when I'm back home on my laptop.