There will likely be covid cases for decades or perhaps it will be a permanent arms race. A small number of cases is not a general health issue, uncontrolled spread is.
We will most likely have to take updated generations of vaccines over time, perhaps yearly like with the flu shots. So the current vaccines won't solve the problem, but they will start a process where we can get on with our lives again, getting back to the new normal.
Until vaccines are generally available, the only meaningful approach is to try to minimize spread. A shame that both US and UK are amongst the biggest failures so far in that regard. With all their financial, educational, and medical resources it is rather strange actually.