Indeed, all Police Officers in the country have their powers throughout the whole country, regardless of which Force they belong to. There are courtesy’s that are usually observed when crossing into another force area in pursuit of a criminal, the control room of the other force is informed (and usually asked for help), and local officers will often take over or lead the pursuit if they are available, though this is more because they know the area better. Upon arrest, the criminal will usually be "booked in" at the local police station but then transported back to one of the original force's police stations for processing. Criminal law is the same across the country, so there is no sense of different jurisdictions. There are some more formalities going into Scotland, which has slightly different criminal laws, but nothing that stops a good chase! Theres no benefit to the criminal of "getting across" internal borders (akin to state lines in the US). Getting across a border externally means crossing the sea, and even then co-operation between European forces is getting better.