Of course you could play it all naive - there's been a complaint made, but I doubt if the council official will have formally told you who made it. So you toddle along to your next door neighbour, say you assume it's some other nosey person who has made the compaint, and ask her if she's had any trouble fom ths unknown other.

There could be a good chance that she'll jump at it, to avoid embarassment, let you go on thinking it's not her, and might even say that she has no objection. Then you can quote her to the zoning officer as having said she's got no objection. (Have a witness.) That should effectively prejudice the officer against her, as a time waster, and they've probably got some kind of flexibility over these things.

I think it's a good rule only to be sparingly open and honest in the case of disputes with neighbours, unless you are basically friends all along, where there's a good chance of clearing the air. And it doesn't sound like you are basically friends in this case, or you'd have talked about what you were planning to do before you did it. (Which is always a good idea anyway.)