I'm not sure the supermarket bags will be deep enough Gattina, the bags you buy to grow potatoes in are a good bit taller, I'm also not sure they would be sturdy enough to survive 12 - 16 weeks outside without starting to degrade. I'd plant all the potatoes at the same time, around two weeks from now sounds good. Roll the bag down part way and part fill with your compost the put the potatoes in and add another layer of compost. As the tops start to appear unroll more of the bag and add more compost until your bag is full. Remember they will need a lot of water in the bags and there also needs to be drainage holes so that excess water can escape. Make sure they are stood somewhere sunny. I do recommend though that you get proper bags to grow them in.

Thank you so much, Moongrower. Lovely straightforward, comprehensive answer.
I did wonder about the depth, but the bags I have are as tall as the biggest pots I have are deep, and the cost of not only buying so many proper potato bags, but shipping them out here (never seen anything of the sort here) becomes prohibitive. I've just had a thought - IKEA bags (the blue sort, not the paper ones) might be deep enough, mightn't they? AND hold more seed potatoes at one go. They are very robust, we haul loads of firewood round in them without mishap, and I have yet to notice any degradation of any sort.
I was really puzzled by the idea of planting the different types at the same time, but it certainly simplifies things, as long as I remember to label them! I have the perfect spot to line them up, and spent yesterday in the hot sunshine clearing it of stones. Given the ridiculously high temperatures we can get here from May onwards, do you think I should shade the growing bags themselves to stop the roots (and the tubers themselves, of course) cooking?

Hi Gattina you plant them all at the same time but will harvest the early potatoes after about 12 weeks and the main crop after around 16 weeks. I had forgotten just how hot it gets where you are in summer so some shade may well be needed. Yes the Ikea bags should work...

Thank you! :o)))))

Hello ... sounds like you may have an infestation of wire worms? They positively love potatoes, and lots of other root crops! Also, I would definitely shade the bag bases or your seed potatoes will cook in situ ... something you don't have to worry about too much if they are in the ground. Cool roots and warm sunny tops!

That's a good idea, Bilbo. I could start them off in the courtyard (fairly sheltered) next to the garage, then take them up the garden when the weather settles down. I was planning to surround the potato bags with the polythene sacks of maturing leafmould to protect against too much sun, but I could even half sink them in the soil, I suppose.
Wireworm were my first guess, too, Avkq, but we didn't actually see any, and I looked up the words our neighbours were using to describe the problem and it said, amongst other things, "mollusc", so, since they are potato farmers (if you shop at Sainsbury's and see boxes of potatoes labelled "Bologna", they probably grew them), we took their word for it and guessed slugs of some sort. They use some sort of chemical to protect their crop, which I am fairly sure isn't a nematode wash, (Far too big an acreage to treat) but didn't look like metaldehyde, but we don't want to go down that route.

Sorry to hear about your disappointing results last year Gattina. When we first started in this garden we were a lot younger and I had to clear ground which had not been used for a long time for growing veg and it was full of perennial weeds and rough grass. The wire worm were only a bad problem the first year. In subsequent years tilling the soil did almost eradicate them. A friend advised using Bromophos which did get rid of them completely but it is no longer available.
You have excellent advice from others so I won't give you more except make sure there are holes in the bottom of the bags to let excess water out. If you could sink your bags in to the soil but using the new compost to fill them that might help with the evaporation problem. Whatever you do place the bags in a square formation rather than stringing them out round your courtyard and that should help to stop any water disappearing as fast as you pour it on. You could sink bottles in to your bags and pour water in that way as I found although I watered in what I thought was sufficient quantities of water when I came to dig my potatoes only the top few inches had had enough water. Potatoes need lots of water.
Thank you for the elevation but just because I am enthusiastic I would not lay claim to any specialist knowledge. I like to listen to advice too. Good luck with your crop this year.

Thank you all so much for your advice and comments. If I don't produce a prize-winning crop this year, I don't deserve to be a GoYer!

All you need is a sense of fun, to be a good goyer, so you'll be fine lol.

Gattina whether your tatties grow or not you are an asset to GoY and one I appreciate!

That's so kind of you, Thank you. Gosh, I've gone all emotional, now!