There are separate companies registries for England and Wales, Scotland and Northern Ireland. A company registered in England and Wales must maintain a registered office in England and Wales and cannot move its registered office to Scotland or Northern Ireland. Incorporation Services Limited can provide a registered office in the country where the company is registered, if required.
A company registered in England and Wales is subject to the jurisdiction of the courts of England and Wales (it is a single jurisdiction) so that any litigation concerning, say the management of the company or petition to have it wound up, etc. must go to the appropriate court of that jurisdiction. Scotland is a separate jurisdiction and the equivalent rules apply to Scottish companies.
On the other hand, there is no legal rule to prevent an English company having a place of business (even its only place of business) in Scotland, or a Scottish company doing the same in England, but it must maintain a registered office in the country in which it is registered, which may be inconvenient.