Visited yesterday; even with the new booking system, I've never seen it so busy (granted, this is the first week of the school holidays). Staff members, and the park as a whole, seem to have done as much as they can to alleviate crowding and general CoVID-19 transmission concerns (I mean, at least whilst balancing their dire need to maximise income), thus kudos to them, but people are people and, well, you can only expect so much outta' the great British public. Social-distancing was largely forgotten (despite repeated staff attempts to enforce). I spotted maybe a dozen folks wearing masks the entire day; about half that number noticeably coughing (without masks) in crowded areas. Yeesh.
There were fairly lengthy queues to get into the reptile house and one-way waterfowl / wolf / 'South America' section. It got better towards the end of the day; crowds started thinning considerably from 3.30-4ish onwards, and by 5pm we found the walled garden delightfully deserted.
And yes! The invertebrate and reptile houses are open, with a one-way system. It worked 'okay' in the reptile house - bear in mind if you want to spend more than a few seconds at any exhibit, expect impatient folks crowding up around you, breathing down your neck. The restaurant, lemur walkthrough, bats, Little Africa, hoofstock houses and parts of the children's farm remain closed.
Otherwise, was a pleasant day. Nothing particularly new to report; I think a couple of the frog species on display near the sifaka have been rotated. The young rhino calf is growing up quickly, and the stanley cranes opposite the camels have only recently had a chick. It's out n' about scampering after the 'rents.
TL;DR / General Recommendations: lovely day out, though crowds nearly everywhere. Best avoid popular sections unless first thing in the morning or after 4pm.