UK Citizen here, my parents have been part of the ONS random survey for about 18 months now, every 2 (or so) they have a visit at their doorstep from the ONS who test both of them, they let them know the results via the NHS app and they get £25 of vouchers for each visit.... They have to be honest about who they have been in contact with, where they have been (E.g. supermarket) and if they wore a mask...

This data goes into modelling for how the government should make decisions about easing lockdowns etc. The UK has some of the best genomic sequencing in the world which is why we are able to identify variants so quickly.

It's just a shame it took the government 1 year to get ready and lied to us in the meantime.

*every 2 (or so) weeks.

The UK is one of the few countries in the world that does have proper randomized studies of Covid-19 prevalence, and has done since close to the start of the pandemic. Unfortunately the results lag behind the actual number of new infections by long enough that we wouldn't expect the drop in cases to cause a corresponding drop in the numbers coming of those studies just yet.

there is some sort of on going testing with a set group that I've been told was randomly choosen.

My sister/ husband and neice (uk based) are currently being tested once a month since the outbreak (mid 2020 ish) and they where told that they was picked at random,

All of them have had covid - and probably would not have been discovered without this testing - since all their cases have been asymptomatic

Cause they’re already at maximum capacity with higher priority projects, I would imagine.

Several municipalities in the US did do randomized sero surveys earlier in the pandemic.

I can’t provide a citation but largely these were abandoned because they were influence by a couple factors

* participation was obviously still voluntary and largely mirrored the same trends you describe

* the data was not short term actionable and took up testing infrastructure at the time

* it was dangerous - I.e., public health workers were threatened, assaulted, and in at least one case shot at.