The U.S. law that provides for fair use is 17 USC § 107.
The UK has fair dealing instead of fair use. (UK gov. description). It is also an affirmative defence. It is less permissive than the fair use standard in the US, requiring that the re-use be from one of four categories of use, and then that that use also be fair (this second step roughly follows the US test).
Canonical answers here: