I'm not sure whether or not my suggestion qualifies as an 'alternative' (which I know that you don't want) or not.
That's because a bit of googling suggests that cannellini beans are either exactly the same as lingot beans (in which case they're what you want anyway) or at least that lingot beans are a specific type of cannellini beans (in which case 'ordinary' cannellini beans then only become an 'alternative').
Either way though, have you tried cannellini beans in your recipes?
https://www.trolley.co.uk/search/?from=search&q=cannellini