depends on which poppy it is.Are you leaving the flower heads on so they form seeds? I dont have trouble with oriental poppies self seeding.
welcome to GoY too.

Silly question from me, as well - you are leaving the heads on, aren't you?

You could try waiting until the head is brown, and then shaking the seeds out yourself, instead of waiting for the plant to do it.

Thats what I do shake the seed head out when its dry

:-))

The only reason I can think of why they won't regrow from seed is that your soil is so hard and capped that the germinated seedlings dry out and wither. Even here where we have heavy clay soil and dry summers, poppies reseed easily, especially opium poppies which come up like weeds.
Try putting a thick mulch of well rotted compost around your poppy plants and the seeds should germinate in this and grow away.

Bertie the soill in cheshire is ideal for them ,it must be something else.