Searching for a similar film...

I'm looking for a film which is slightly similar to BLIM - well not really, it also involves a kidnapped/ missing child but it's a much more straightfoward British mystery film.

I can't remember much about it, but the first scene involves a woman, who I believe is the nanny of the child rather than the mother, going into a (chemists?) shop and leaving the pram with the child in outside. When she comes back out the pram and child have been taken, but no one has seen anything suspicious.... the rest of the film then follows the hunt for the missing child and eventually everything is nicely wrapped up in the end.

I have a vague recollection of the final scene, where the police have found the child who has been kidnapped by a crazy woman who walks out with the infant in her arms to the edge of some cliffs and seems ready to throw herself off but is eventually talked down.

the film is b/w, probably British and dates from c.1950-1965.

I think the film is actually fairly well known, not a mega obscure picture no one has seen, but my memory has totally failed me and it's been years since I saw it. I've tried all manner of different keyword plot related searches here and on google but to no avail - does anyone have the faintest idea what I'm talking about?

Thanks in advance!