What is (if there is one) the equivalent of the tenure-track phase in Europe?
In the UK there are four levels of permanent academic employment: lecturer, senior lecturer, reader, professor. These four positions between them are roughly equivalent to the three US positions of assistant professor, associate professor, professor. These days lecturer is often a probationary position for the first few years, but higher positions are permanent. Promotion to senior lecturer does not follow automatically upon being confirmed as a permanent member of staff. Apart from this practice of probationary appointment there is no formal tenure system. In my experience (which is limited to mathematics departments) it is quite unusual for probationary appointments to not become permanent.

In my understanding, not very long ago senior lecturer and reader were seen as roughly equivalent, but senior lecturer was seen as more heavily emphasising teaching and administration whereas reader was seen as a position which more strongly emphasised research. However, there is a developing tendency to see the two positions as having essentially the same nature, with reader simply being more senior.

Some British universities are in the process of adopting the three-tiered U.S. nomenclature, but such universities remain a minority at present.