Abandoning (deserting – see s 14 Animal Welfare Act 1999) a cat is an offense but unfortunately it happens all of the time for many different reasons.
In the first instance, contact your nearest SPCA centre.  It is important to note that language can be important – the cat has been deserted, and you have not fed them.
If you have no luck via this avenue, get in touch and we’ll see if we can help.