This is not as easy as it sounds. There are at least three easily-found types of cat racing: racing of vehicles sponsored by the Caterpillar company, racing of catamaran sailboats, and racing of felines. And, when you do find something about racing felines, it's an ESPN Magazine April-Fools joke involving lots of bad puns.
But, no, apparently cat racing was a real sport. This site quotes an 1889 cat book, which quotes "The Pictorial Times" of 16th June 1860: "Cat-racing is a sport which stands high in popular favour. In one of the suburbs of Liège it is an affair of annual observance during carnival time... The cats are tied up in sacks, and as soon as the clock strikes the solemn hour of midnight the sacks are unfastened, the cats let loose, and the race begins. The winner is the cat which first reaches home, and the prize awarded to its owner is sometimes a ham, sometimes a silver spoon. On the occasion of the last competition the prize was won by a blind cat."
This raises the obvious question, as discussed in this brief exchange:
brooksmoses: "I'm not completely sure how they determine which one gets home first...."
ibnfirnas: "Bar fights."
The above site further goes on to note that, in Dorset, England in 1936, a 220-yard-long cat racetrack (much like a greyhound track) was built, and was equipped with an electric mouse as a lure. And, further, there was some attempt to race cats in Kent in 1949. Both of these were apparently commercial failures; it appears from suzanne's description that Mad Jack is set in a slightly speculative world in which something like the Dorset track was actually a success.
And this, of course, is why good writers seem to savor the weird things in backwaters of obscure historical books: it's all material.