As an example, if I want to run a takeaway service with just one chef physically in the premises with nobody else working inside with a delivery driver waiting outside to receive goods and deliver them, would this be permissible?

The main thing to remember is that more than one person cannot be inside a premises. If a delivery driver was to wait outside the premises at a safe distance and if all hygiene guidelines were strictly adhered to then this would be acceptable. There should be no physical contact with colleagues or customers with goods left outside of customers' homes.