A copy of the employers liability insurance must be displayed at the premises insured - nothing to do whether you're a business or not.
Yes, I agree. The requirement to display the employer's liability insurance comes from the Employers’ Liability (Compulsory Insurance) Act 1969 so it's not a question of whether you're a business but whether you're an employer. However, allotment societies will often have employer's liability insurance for their volunteers, and volunteers aren't employees so there'll be no requirement as such to display the certificate.
And if you take part in any activity off the premises - plant sales at school fetes, for example - a copy of the public liability insurance must be displayed (and given to the organiser).
I'm not familiar with this. Where does the requirement come from? Is there an actual requirement to insure these kinds of events?