There's a bit of use of "farm_auxiliary" as a key rather than as a tag: https://taginfo.openstreetmap.org/keys/farm_auxiliary#overview 

I know that farmers in at least one country (not the UK) were unhappy at the overly specific tagging of sheds and barns (they were worried that thieves could identify were machinery was stored).  However, I doubt that that's an issue with mushrooms!