The short answer is 'no'. Having a business use vehicle insurance policy will not normally cover you for making deliveries of any kind. If you are a food delivery driver, even if only a part-timer, you will need a courier insurance policy that specifically allows you to deliver hot food to multiple locations.
Who needs business insurance?
Many people think that adding commuting cover to their standard SDP (social, domestic and pleasure) policies allows them to drive to several different places of work; but it doesn't. it covers the policyholder to drive to a single regular place of employment; or to a parking area from which the policyholder catches public transport to that single place of work.
Anyone driving to more than one location for work; such as someone visiting more than one branch of a company; would need business insurance.
For example: let us consider a social worker. If this person works from a single office, care centre, hospital, or any other type of establishment, commuting cover is sufficient. However if duties include visiting clients, then business use it necessary.
Similarly, accountants, out visiting clients; or even cleaners and care workers who carry out work at more than one address; need this class of insurance; even though it appears that very few realise it.
There is a higher level of business insurance called Class 3. This allows the driver to travel, possibly without making an appointment, to multiple locations throughout the country, carrying samples if necessary. Even this level normally excludes cover for the delivery of any goods; for instance a travelling sales representative, taking an urgent order to a customer, could be accused of driving without insurance, unless a policy which specifically allowed this was in force.
So no; business class vehicle insurance will not cover you for delivering any goods whatsoever, including food, unless there are specific additions written into the policy (and we haven't seen one yet). You will need to buy food delivery insurance.