Actually, technically, "in the UK" there's no such thing as breaking and entering.
In Scotland there is. In England and Wales there is not. Instead you'd be charged with criminal damage for whatever you broke getting in, or of course burglary if you go further and steal something and/or assault someone.
In this case, as you quite rightly say, nothing was broken so the only offence is trespass and that is indeed civil.
As for Northern Ireland... I don't actually know... Google time for me.