Hi valerie,
Thought the council may say that if it was a dog it would be different,as i said earlier if you or a member of your family took the cat to a rescue centre out of the area to be rehoused,the cat would probably be happier not having to stay out all night,your life would be happier(and this is FAR more important than a cat).
You could just say you found the cat,it sounds to me like the neighbours would not miss it.
As for awaiting the cats cries every morning then i think from experience this maybe true,we had lovely next door neighbours until they moved and a family moved in,he went to work every morning at 4.30am and had a full on argument with his misses at full volume in the bedroom joining ours,and when in on his own blasted dance music at unbelieveable volume,we went around and asked him to turn it down but got same response as you,all this made my wife very ill and be at home a nightmare.
As suggested when i used to come home and they where in i was constantly on edge wating for the music/shouting to start,the problem has now gone away due to a tragic accident,sorry to go on a bit but i know how it feels to have selfish,inconsiderate people spoiling your life and it should not be allowed.
Andrew.