So in the UK/Met it really depends...
Boroughs
If a CAD (computer aided dispatch) is set up post a 999 call, it will be circulated to the response team in the correct borough. There may be times where the control room arn't entirely sure and you may be sent to a CAD that's on the border, but that is unusual.
Proactively, you are unlikely to deal with something that's not in your borough, unless it's something you can't ignore. For example, I was escorting a prisoner through Westminster, when I saw a bloke beating up his wife. I can't ignore that, so my colleague shouted at the prisoner to not do anything stupid as I jumped up to deal with the domestic violence. In that case, I handcuffed him, but did not arrest. We then waited for a Westminster officer to attend, who then arrested and dealt with it.
If it had been a proactive drugs stop and search, or a beggar or something low level, Westminster probably would be like 'why did you choose to deal with it, to then hand it over to us'. So I would probably end up taking the arrest, investigation to the end.
A different example: Bloke was seen recklessly driving in Westminster, before he drove into Chelsea. So the CAD that was set up was a Westminster CAD. We got the bloke, who turned out to be a burglar/a million other things. He got nicked for 8 different things. We stated that it should be dealt with by Westminster officers, but Westminster Officers handed it back to us as the arresting officers. So there's a certain amount of haggling.
Partner Agencies: MI5/Immigration
This is where we differ predominantly from the Americans.
From what I know (I'm not a terrorism officer!), the Met do the grunt work, the Security Services lead. Take the example, where they're storming a house to arrest someone for terrorism offences. From what I understand, they generally prefer that the Met do the arrest/door kicking/vigerous shouting etc. They may be there, or they may be in the control room.
This also goes for Covert Surveilance (following people). The met does a lot of what you would consider anti terrorism. Which is kinda the advantage of being on home soil. Abroad, MI6 have people doing a lot more, though it depends what the relationship is with the country. Huge difference between, if the country is generally hostile to the UK or if they are friendly and you're working together to identify mutual threats.
Immigration Service: we generally identify and arrest people, at which point we refer them off to Immigration. Immigration arrive at custody and take the person off to one of their faciltiies etc.
It's worth noting that the specialist services don't have a huge amount of people. They certainly can't turn up to a major or critical incident and be like oh yes we need 50 agents to close roads etc. They will almost certainly use the local force for this.
Command
It's worth looking at the above two terms.
Major Incident: Any incident where more than one emergency service is required. So a horrific fire may well require London Ambulance Service, Police to do road closures, crowd control and obviously Fire Brigade.
Critical Incident: Where the public confidence in the Police will be effected. Example: Steven Lawrence murder which had huge ramifications for the publics view on policing. Unlike many other murders which however horrible, did not have that impact.
It strikes me that both will become very relevent in your story.
General rule: the most senior person present of the most appropriate service.
So in our above example of awful fire, you would expect the most senior London Fire Brigade official to be in command.
If you had a riot, whilst ambulance staff may be needed, the Police will be in charge.
If you had a scenario where there happened to be a Police Superintendent present at a fire, whilst the fire brigade had no one of rank present, the Superintendent would have more of a leadership role, until someone representing the fire service arrived.
Your scenario:
Terrorist attack breaks out.
If I assume that supernatural people rights are a hot topic, not to mention interesting for the press. I would expect it to be declared as both a major incident and a critical incident.
Depending on how well staffed your Ambulance service is in your world, I would expect the Police to arrive first.
Police Arrive: they will start: Applying first aid, closing roads, crowd control.
They will want to shut down the area and create a rendez-vous point and consider access and egress. They may well park their vans/cars to block traffic, but you need to have a route in for everyone arriving AND a way out of the cordon for predominently the ambulance service who need to get in and out to hospital.
At this point, you'll have a Sergeant on scene who has probably called the duty Inspector down as well.
Then you'll have everyone else arrive:
If terrorists are still running about, then ambulance staff may have to wait until they're neutralised. I don't know if your event is:
1. a bombing where the terrorist has escaped.
2. an attack, where armed terrorists are running about.
You've stated that SID are more like the FBI. By this I assume they are doing the investigation not the bad guy killing. If your supernatural threat is so scary and powerful that the Police can't deal with it, then the Police will control the area and call in the army- who presumably have a supernatural management unit.
A good example here is that the Met is the only UK police force to have their own bomb unit. Other forces call in the army to do it, so they'll cordon off the area and then the army team will go in to deal with the bomb.
The Major incident will likely have a team of people managing it:
SID Rep
Ambulance Service rep
LADO (Local Authority Designated Officer)
Fire Service rep
Police Rep
Now, I would suggest that whilst the SID especially if they're used to A. not working with others and B. working in secrecy, may want to be in charge, they may not be.
1. If they've previously worked in secrecy, I suspect they will have no understanding at all about how other services work. Ergo, are in a poor position to co-ordinate a multi-agency approach.
2. their skills are in investigation. Investigation comes after. The foremost priority is to save lives and then to preserve evidence.
I would suspect that whilst it is a live major incident, the Police would be in charge, with the SID person advising, along with list of other people.
Once the situation is controlled, all the injured people have been evacuated, terrorists apprehended, monsters shot etc. The Police would hand the scene over to SID for them to sift the scene for clues that were missed.
Hopefully some of the above is of use/interest
Pentagon
There's definitely potential for conflict there though.
