Then there is cross-over immunity, where there are anti-bodies from another coronavirus infection that protect against COVID,
Put it all together, and it may be that 80% are immune like Wyttenbaxh says. At this stage though, it is all guessing.
The problem is cross-over effects cut both ways. The near matches can prevent normal antibodies forming but provide no protection. So we don't know this effect.
There has been enough evidence to show the T-cell effect - and we know COVID is unusual in stimulating T-cells - they seem much more important in successfully fighting it than for other diseases.
The Diamond Princess gives us a limit (for that population) on immunity: 3000 people, 712 cases => At MOST 77% immune. that assumes that everyone on the ship was exposed enough to catch the virus - unlikely.
In addition, when we talk about immunity, we probably mean partial immunity. A small dose infection might be fought off, when a larger dose would not be so.
Another reason to think immunity is not so very high is just the high R0 numbers. If only 20% of contacts can catch it the high reproduction rate it has ben showing seems unlikely?
A lot of uncertainty because previous exposure immunity could be very variable across populations. The best prophylatic probably is a few CV colds - difficult though to get them right.