On reading we are in national mourning and not knowing what exactly this means, apart from flags flying half mast, I checked the government website. It says that all and any business, etc is able to close during this period if they wish to do so.
Thinking about the RHS, they have particularly close ties to the Royal Family and many of their staff must have met the Duke and felt they needed a day to mark their respect.
I know this doesn’t help those who were looking forward to a long awaited visit, for whatever reason, and I hope those with bookings will be given priority as soon as possible.