Even if you don't have detectable levels of antibodies - if you've been previously infected or vaccinated - you will likely have robust and durable immunity that greatly reduces the risk of hospitalization and death [1][2][3].

[1] SARS-CoV-2 infection induces long-lived bone marrow plasma cells in humans https://www.nature.com/articles/s41586-021-03647-4.pdf

[2] Longitudinal analysis shows durable and broad immune memory after SARS-CoV-2 infection with persisting antibody responses and memory B and T cells https://www.cell.com/cell-reports-medicine/fulltext/S2666-37...

[3] Rapid induction of antigen-specific CD4+ T cells is associated with coordinated humoral and cellular immune responses to SARS-CoV-2 mRNA vaccination https://www.cell.com/immunity/fulltext/S1074-7613(21)00308-3

I'm curious how they got this number, considering "Antibody tests are not widely available yet" according to NHS (https://www.nhs.uk/conditions/coronavirus-covid-19/testing/a...).

You can follow some links on the page you linked to and end up on one called "COVID-19 Infection Survey: methods and further information". This is a direct link to the section "Sampling" there:

https://www.ons.gov.uk/peoplepopulationandcommunity/healthan...

The UK surveys the population regularly.

https://www.ons.gov.uk/peoplepopulationandcommunity/healthan...

Why stats says that the vaccination rate in UK are 62% (https://g.co/kgs/jnTxhM) and this post say that is 80%?

It's probably 62% of the entire population including children, and 80% of adults.

they sure have a lot of new cases for a place with almost 100% immunity

https://www.worldometers.info/coronavirus/country/uk/

Not 100% immunity - a high level of people with antibodies.

This doesn’t give you immunity, but means that you are less likely to catch it, if you do catch it you are much less likely to need hospilisation and even less likely to die from it.

The rates of hospitalisation are creeping up, but at a significantly lower rate than previous ‘waves’.

Finally.