Thanks guys!
I followed Bushfiva's advice and looked at all the card-in-slot machines at varying prices and availabilities.
Went to our local Dixons and they had a version of Kobo with a card slot and, hurrah, it runs without creating an account or logging in.
Within five minutes of getting home I had put a book on card and was reading The Picture of Dorian Grey at the same point I left off when reading on my tablet.
Sorted! Thanks!