Most ped zones have an “except for access” exemption, if only during the middle of the day between peak periods. If there’s a rear service road there’s no problem as people can still get to their properties that way. Otherwise, you might well get justifiable objections for cutting off people’s vehicular access to their properties for the entire day. And possibly if would force loading to occur at antisocial times, causing a noise nuisance.
However, there is a get out if you need one. Subsection 2 of s3 says that you can still prohibit vehicles for more than 8 hours if you deem it necessary “for avoiding [or preventing the likelihood of] danger to persons or other traffic using the road to which the order relates or any other road”. So provided you can say that it would be a danger to pedestrians to have even the limited access traffic in the road during the middle of the day, you can use this subclause to over-ride the first one you quote.