I'm surprised that it doesn't set seed. This is commonly known as Welsh Poppy and has a reputation for being a bit of a nuisance as it's a prolific self seeder.

Having thought about this dilemma and allow it to self-seed where it is in the paving stone this is what I would do:-

I would split a shallow but wide plastic plant pot down one side, place it around the bottom of the plant and fill it with soil. This will create a mini soil bed around the plant which hopefully will catch the seeds and they will germinate. Keep it well-watered so it doesn't dry out and remove the pot once the seeds sprout.

Judging by the fact that the seeds for this are available one has to assume that it comes true from seed.

This question brought a smile to my face as they are all over my garden. Lovely as they are, I often pull one or two up. Now they are all over my friend's garden and the one where I work. Good luck with yours Wendy. I'm sure you will have success if you follow Myron's advice. In a couple of years you'll be digging them up too.