If you are a plumber or deal with plumbing then it is highly recommended you have public liability insurance for a plumber to cover your liability should the unpredictable happen. Plumbing requires very precise work and even the smallest of mistakes could lead to a leak which in turn the customer would hold you liable for and try to claim any costs for the damage from yourself, this is the point that you would usually turn to your public liability insurance.
If you were working on a site alongside other professionals such as carpenters in the production of a kitchen then the main contractor may insist that you have a public liability insurance policy in place before you are allowed to actually do any work.