There are two types of insurance that a delivery driver needs to consider.
If a driver is carrying goods that belong to someone else, and is being paid for it, then hire and reward insurance is necessary. A normal car or van insurance policy will not be sufficient for this type of work, which could indeed render a policy like that null and void.
The next one would be goods in transit insurance. If a driver had an accident and goods were damaged, or if they were lost as a result of theft or negligence, then the owner of those goods would be perfectly entitled to sue for the full cost of replacement, as well as associated costs. Thefts from delivery drivers are unfortunately running at an extremely high level, and many of them occur when the vehicle is left unattended for a moment whilst the driver makes a delivery. Sometimes this can result in very expensive losses, and without proper insurance this could all be borne by the driver.
Whilst goods in transit insurance is not a legal necessity, it would be very prudent indeed for a delivery driver to be protected by it.
Neither of these policies, of course, are necessary for people who are carrying only their own goods, such as grocers carrying their own produce to market, or builders taking their own tools or materials to a building site.
The premiums for these types of insurance are very much an individual matter because everyone is different; with different types of products delivered, different driver profiles, and different vehicles so it would be necessary to talk to a specialist broker who would be able to advise on the best policies and the lowest premiums.