As with all things like this, it's complicated.[0]
It used to be the case that the right did not exist, but there are now provisions that allow cross-border arrests under 'urgent' circumstances even if there is no arrest warrant. This is confounded by the fact that some crimes do not exist or have different names or are classified differently. So, if I was North of the border in possession of an air rifle without a license, and was then chased by a Scottish Constable across the border into England, well... I have no idea if they could then detain (that is, arrest) me, since in England air weapons do not require a license. Anyone curious about this should try the experiment and report the results...!
It used to be the case that the right did not exist, but there are now provisions that allow cross-border arrests under 'urgent' circumstances even if there is no arrest warrant. This is confounded by the fact that some crimes do not exist or have different names or are classified differently. So, if I was North of the border in possession of an air rifle without a license, and was then chased by a Scottish Constable across the border into England, well... I have no idea if they could then detain (that is, arrest) me, since in England air weapons do not require a license. Anyone curious about this should try the experiment and report the results...!
0. https://assets.publishing.service.gov.uk/government/uploads/...