There was a movie from 1955 called A Kid For Two Farthings, filmed in London, about a boy who bought a baby goat with a single central horn believing it to be a unicorn. The zoo isn't listed in the locations for filming (on IMDB) but it could be that one.
I vaguely remember seeing Cinema hordings for this film though I did not see it.
Two other mainstream films, both from the 1960's, I remember that feature Zoos were 'Morgan, A Suitable Case for Treatment', starring David Warner. An early scene was filmed in the London Zoo Monkey House. And 'Hannibal Brooks' starring Oliver Reed, early scenes shot in Munich Zoo as it was about an Elephant supposedly led across the Alps during wartime. Apparently its based at least in part on a true story about an elephant rescued from Vienna Zoo.