Please remember that it is not a matter of being 'allowed to re-open' as the Government has said zoos were never asked or required to close in the first place, and could have been open all through this.
The issue is that the zoo visitors are not allowed to travel, so there is no point in the zoo being open because its visitors could not travel to it.
Driving to Tesco's, and now B&Q, or into the countryside to walk your dog or ride your bike is permitted travel and OK, but driving to a zoo to walk around it, is not and subject to a cumulative fine. This contradiction has to be addressed before a zoos visitors can visit again.
The latest Government FAQ does seem to contradict what you’re saying here. According to the latest update you still cannot visit a ticketed attraction.
Coronavirus outbreak FAQs: what you can and can't do
The language used by the Government here indicates that it has not been possible for people to visit ticketed attractions since lockdown began. Meaning zoos do require Government steer on when they can re-open to visitors.