I believe that an officer of the Metropolitan Police or British Transport Police could just as easily arrest a person within the City of London (which has its own police force) as one of Surrey police could arrest a person in Kingston-upon-Thames (which is not in Surrey).
But can Welsh police enter England and vice versa? Scottish enter England and English, Scotland?
How are British police powers limited by intra-U.K. jurisdictions?
Within the united-kingdom there are england-and-wales, scotland and northern-ireland.
Broadly speaking:
A police officer from one country can cross a border into another country to execute an arrest warrant issued in the 'home' country. For example, a Scottish officer may arrest a person in England who is wanted on a Scottish warrant.
A police officer may cross a border to arrest a person for an arrestable offence that occurred in their 'home' country using their 'home' powers. For example, an English officer may pursue a person suspected of committing an arrestable offence in England into Scotland and arrest him under English law.
A Scottish officer who happens to be in England may arrest a person suspected of committing an arrestable offence in England in accordance with English law, and must take the person to an English police station. Likewise for an English officer in Scotland and so on.
See Cross-Border Enforcement, Part X of the Criminal Justice and Public Order Act 1994.
Also there is provision for cross-border assistance at s98 Police Act 1996. If for example a chief officer in Scotland applies to a chief officer in England for aid, the English officers go to Scotland and operate under Scottish law.
