Honesty, or lunaria annua. It has beautiful purplish flowers in late spring or early summer and then those distinctive seed pods that are themselves decorative. There is a white variety which is even prettier. Dead easy from seed and self seeds readily.

Agree with Bertiefox. Soak the seeds and add to compost and they should germinate then self seed. Nice plants esp when dried as you have found. They remind me of my childhood - my mum had them in a vase and I used to take the seeds out and grow them.

Spreads like crazy Johanna be warned ,once planted it will be with you always !

Collect the seeds and plant them in an area where you would like a group of them to grow and you will have a few plants next year. Lovely in a group. Some people call the seedheads " honest pennies" because the popular name for the plant is Honesty. They are in flower right now.

Its a biennial so usually flowers in its second year though you might be lucky with some.

Thank you all for your very helpful advice...I'll sow some in a patch outdoors straight into the soil and some in pots on the windowsill (for a comparison!)...Considering I knew nothing about this plant just 2 days ago and now got a bit of info and a good start for trying to cultivate some more... I'm so delighted....And I only happened upon this site by chance, not being a very experienced gardener...I can see it's going to be a useful bit of help for me : )