Baby MPS is a free service which allows you to register not to receive baby related mailings.
By checking the information Baby MPS makes available to them, companies are advised how your circumstances have changed as well as your preference not to receive further mailings about baby products and services.
Since Baby MPS information is updated daily, companies have access to the most up-to-date information possible.
They will, of course, respond in a sympathetic way, and remove your name from their mailing lists. For you, it means you will still get the post you want. You'll just receive significantly less of the post you don't want.
(It's important to note that companies who are not members of the Direct Marketing Association and Baby MPS may not be aware of your circumstances, and may have to be notified directly by you.)