There isn't a comprehensive answer to this, as each force had its own structure prior to 1964. There were 'county' police forces and individual boroughs had their own forces too. Jurisdiction was finite however... theoretically, however in practice relations between forces varied, depending on individuals within the structure and 'culture'.
As a rule forces worked together well, but information exchange was virtually non-existent, except when requested or as a courtesy, mainly due to the low-tech and 'paper' culture, rather than as policy. It was considered polite to inform another force when your investigations took you into their territory and often a local officer would be assigned to assist. Otherwise, requests from other forces for information/apprehension etc, were treated as promptly and efficiently as were their own (whatever that might be!).
The CID was effectively a parallel organisation in each force and was theoretically the 'elite'. While the uniformed branch dealt with the day to day stuff and serious crimes that were immediately detectable, the CID worked on the 'long game', or conducted the investigations following apprehension of criminal suspects by uniform. Each force had its own CID, which was headed from (but not necessarily based at) force headquarters. There was a general rivalry between uniform and CID, which was sometimes more intense the higher up the ranks you got.
Each Division had its own separate CID Division (i.e. 'A' Division CID etc) and teams were based within individual sub-divisions, or even stations in larger towns and cities. Specialist teams were 'force-wide', but other groups had their 'own turf' or 'manor' and could be quite territorial with regard to other CID divisions (or even stations). There was often a 'cult of personality' within each group or team too and top detectives were often rivals to their fellows in other areas/Divisions etc.
A DCI was the effective 'line manager' and would head the CID of individual stations. He would have one or more DIs under him, who themselves would have one or more DSs under them, each with a number of DCs each. Within a sub-division, the CID would be headed by a Detective Superintendent and each Division by a Detective Chief Superintendent. There was no rhyme or reason to this, the rank went with the post, so you might get a DCSu in a city force having a few hundred men under him, while a rural one might have less than a hundred, with a similar structure down the line.
You could even have a DCI running one DI, who himself ran one DS and a DC, in the Divisions of one of the smaller forces. As a rule of thumb a DCI was likely to be the highest ranking officer to be working a case, but more usually it would be a DI reporting to a DCI.
If a CID was felt to be outside of its depth, specialists from other forces might be requested. In contemporary fiction, it would be someone from 'Scotland Yard', but it could be someone from anywhere in reality. Even more rarely the services of a civilian might be employed for their specialist knowledge.
As for river forces and suchlike, I'm less clear on. The Thames River Police pre-date all other police forces in the UK, so could well be a special case. The usual arrangement is that a specific division within a force was created for something like that.
I hope that is helpful.
18 October 2022, 11:32:37 PM