Source: I was the desktop tech lead consultant during another police force's Windows XP migration
Multiple reasons for the long delay:
Internally the police use alot of bespoke software, either written specifically for them by a 3rd party or their own in-house devs who have long since retired, left or been made redundant. Try finding a download link to Windows 8/10 drivers for a taser. for instance.
All of their builds need to be signed off at the highest security level, ditto for any changes then made. It's a process of producing a build, getting it signed off, getting it tested, having a change requested, making the change, getting the whole build signed off again etc etc.
I don't know about MET however in my force they were also trying to implement hot desking at the same time, so we also had to engineer and deploy full data/environment/application roaming at the same time as the operating system upgrade.
And finally; why not go straight to Windows 10? Because the contracts for the XP migration were all signed years ago before 10 was avaliable. It's taking this long just to get on to 8.1.