The following website, makes the claim that only one ship was sunk in all of the ships within convoys escorted by blimps during WWII.
Googling yields a bunch of excerpts claiming “no ships”.
One thing I did not know before reading the linked site, was that blimps utilized MAD technology to identify submarines traversing chokepoints like the Straits of Gibraltar.
MAD technology?
Magnetic Anomaly Detection. Basically, you drag a sensitive magnetometer behind an aircraft and try to detect the presence of a large hunk of ferrous metal, like a submarine. It works even if the submarine is submerged. The only problem is that you have to be quite close to the sub; this site claims a slant range of 500 meters from the detector. OTOH, this .pdf from a MAD systems manufacturer claims 1200 meters. Though they don’t mention ranges, some idea of the electronics involved in the newest publicly-known stuff can be found here. So, it’s not good for hunting subs on its own, but very useful for pinpointing them in the last stages of an attack, or when their freedom of movement is very restricted, like in a strait.