There are situations when copyrighted material can be used without breaching copyright - eg. quoting parts only, research etc.
I assure you Al, any private letter or text message is copyright material unless the author has given permission for its publication.
It is not a criminal offence, but the copyright owner can sue for its use to be stopped and for any damages.
There may also be the matter of breach of trust if an understanding existed (expressed or implied) that PMs remain private. In a Cllrs case, that could be a serious breach of the code of conduct to publish private correspondence (unless there is a public interest defence). This could have other consequences for anyone holding other public positions .....