http://www.imcdb.org/movie_17483-Tramp,-Tramp,-Tramp.html

All pictures from youtube

In a coast to coast walking race movie , logically, you can see very few cars. I have only found this one and I don't know if it is the Checker Model F requested in main page. I only can add that is a taxi car in the scenes I have seen.
Here too background

And more partials views