The Watersons sing a song called 'I Went To Market'. I don't know if it includes a cat but the verses all start
I went to market to buy a [hen, pig etc.]
And the [hen, pig etc.] did very well please me
Every time I fed my [...] I fed him all under a tree ...
The list that follows at this point grows longer with every verse - like Old McDonald. I'm not sure I have the words but if it's any help I'll try and take them down and send them. - Susanne