The general public has little comprehension of the basis of scientific experiment, it appears. It is essential, repeat essential, to ensure that every single person in the country has been tested, and also to close the borders securely, before there is any way to know how many of them, at a given time, have a shared characteristic such as a particular infection.
Some countries did that. U.K. did, if anything, the opposite.
Two things are needed in order to have reliable figures on how many people from a meticulously tested population have been left immune, after asymptomatic infections as well as the others. First, of course, repeated whole-population testing. But also, exposing that population to sources of infection, to see if they resist or not. That would need a country first to eliminate the infection and then deliberately to flood it with infected people, with no measures to prevent transmission. That won't happen. Therefore, the true re-infection rate will never be known.
It would be possible to set up experiments with a statistically significant number of those who have tested positive, including those who were seriously ill and those who were picked up as positive by chance, on random testing. They could be introduced to a dose of new infection inserted into their noses or throats.
But it would be likely to be considered unethical, particularly because second infections were often worse, and even fatal, in those freakishly rare situations, where it is known for certain people have had one case, have become clear of infection, and afterwards had a second infection. These are rare because of the absence of whole-population testing and not, not, not because of their true rate.
Incidentally is is possible to check for certain that the new infection is a totally new one, even if shortly after the first, because the 'fingerprint' varies.
So no, having had it once gives no certainty of any protection whatsoever. And this disease is unusual in that the second infection is often worse, repeat worse, than the first. The injection is not even aimed at preventing infection. It merely is hoped to make an infection less severe, particularly in the extremely vulnerable groups.
The immunity such as it is may be fleeting, but it is hoped it will have had the secondary effect of giving the body's own defences a wake up call.
Now, with a far more easily transmitted second virus known to be sweeping through parts of U.K. and Europe, and an even more serious variant coming from South Africa, there is a lot to worry about.
People wearing masks under the nose or not at all, people believing the fantasy that having had it once has made them infection proof, and people believing the entire population can and will soon have a magic injection making them something akin to bullet-proof, are a risk to the lives of others.
In case there are still people thinking 'others' don't matter, because only children and young people count, please be aware that children and young people are apparently more likely to fall to the second variant and especially so with the third, the South African variant.