"White glue" comes in different forms, but the permanent version is basically a "PVA" or "vinyl" glue, very like acrylic paint. In the U.S. at least, any glue that says "school" or "washable" is not permanent though so may not work for some things (like slime?).
Elmer's is just the best known brand name here for white glues (they make the permanent type which is called Glue-All, and the non-permanent type called washable "School" glue... though they can both be used in schools of course).
White glues are water-soluble when still wet, but the permanent ones will become highly water-resistant after drying, and esp. after curing (about a week). Some permanent "industrial-strength" ones come close to being totally water-proof, but most will still soften and give a little if they're actually soaked for awhile.
I'm sure you have lots of "white glues" in the UK, but you may not have the brand called Elmers, which shouldn't matter.
Just look for an inexpensive white colored** glue at your craft or hardware or other store, and make sure it's permanent if that's what you need for your slime. "Tacky" glues are also white glues that are thicker and therefore have more initial grab, and other brands of white glue may be stronger after drying or thinner or sold for specific purposes such as for making books... but still all are "white glues."
** carpenters' "wood" glue" is also a white glue, but it's been colored yellow
And vamsy, that was interesting about the Cascorez (sp?) glue, and explains something entirely different to me.... thanks!
Diane B.