At current infection rates in the UK and the US, we won't see "herd immunity", defined as 70% infected with Omicron, until sometime in November

The US is averaging roughly 720k infections per day, and the UK 147k, so far in January.

In the US you have to have roughly 232m people infected to get to 70%. At the current rate of infection, that's 322 days.

In the UK you have to have roughly 48m people infected to get to 70%. At the current rate of infection, that's 327 days. 

There is no way to predict if current rates of infection will persist, but current rates put us to mid-November.

One thing's for sure, however, the vaccines sure as hell aren't stopping it.