THank you both for suggestions! We have talked to the neighbour and as we are not in during the day, the best we can work out is her cat staying in on a Monday and Tuesday, and ours Weds, Thurs, Fri. But I don't think she's willing to commit to this long-term. How do you cat proof a garden? We have fences on either side, and a wall at the back... but it does seem a bit extreme. Do you think it will sort itself out if we leave them to it? I just feel so bad for our little cat! I would keep him in, but he goes a bit nuts. He needs to go out, I think.