.jpeg)
Most UK police officers are employed by Police Scotland, the territorial forces in England and Wales, or the Police Service of Northern Ireland. But, regardless, they all have jurisdiction throughout each UK nation in accordance with "local" policing powers — which aren't much different.
In the UK, officers will continue pursuing someone across an area border but would probably contact the other force for assistance in apprehending the suspect if appropriate. They may also travel out of their area of employment for any reason to exercise their applicable policing powers — which aren't that much different in terms of criminal law. However, in the US, policing is notably different with a vast majority of local police officers being confined to their departments' attested cities and towns, counties, villages, and states — a major difference to the country-wide powers of officers in the UK — unless permitted by the other area's police department. The FBI is the only US police force with country-wide policing powers, according to the Federal Government of the USA and its Department of Justice.
When a major incident occurs, several different (UK) police forces have been known to respond and work together in a desperate attempt to protect citizens' lives — which would shock many foreign police officers and possibly even their chiefs.
The Gardai is quite similar to the police forces of the UK, as they reportedly have jurisdiction throughout the entire Republic of Ireland. However, because they're not attested by a UK police force, their powers don't apply here and cannot be used in this country without permission (or a warrant) despite the strong similarities in legislation.