In the United States, we use the title Professor or Prof. (in writing) for all faculty at the assistant, associate and full professor levels.
In the United Kingdom, we use the title only for the most senior level of faculty.
So, if an assistant or associate professor from the United States moves to the United Kingdom, should they stop using the title? What if it is for a short time (like a semester sabbatical?)
I can see an argument for both sides. On the one hand, if you use that title in the United Kingdom (especially in writing) others will assume you are a full professor, which could be considered misleading. On the other hand, other titles are kept: in the United States, people still say "Sir Patrick Stewart" even though the "Sir" doesn't have any official meaning in the United States.
There is a related question here but it doesn't address the issue of moving from one place to another.