Many thanks for your enquiry regarding ring pots of the past! I’ve seen various growing methods and systems in my time but I can’t recall any ‘whale hide’ or ‘lino’ growing pots – but I might still be able to help...

I have used Growpot rings - the modern day version we stock - with great success and although they’ve have been designed with growbag production in mind (they are sold in sets of three with a serrated bottom edge to cut neatly through the plastic), there’s absolutely no reason why they can’t be used in borders and open soil. They last for years as well! 

An alternative we used to stock were the lightweight, budget version of one-use ring pots made from a biodegradable fyba material. They were supplied by well-known compost producers J Arthur Bowers and I’m sure they are still available from some outlets; I raised the greenhouse border-grown tomatoes in our Stephanie’s Kitchen Garden project with these for a couple of seasons and they might well be the nearest current version to the product you remember. 

I’m sorry not to be of more direct assistance on this occasion but I hope I’ve been of some help; many thanks once gain for your enquiry and happy growing this year!  
Martin