I see the bobbies with the tall hats and the cops with the checkering on the hats. What the difference?
I know in the past the bobbies where un-armed but has the recent situation changed all that because I see the checkered hat guys with weapons all the time.

many thanks from your brothers in the states

I think the cops with the tall hats are foot patrol police and the others with the flat caps are mobile ( you cant sit in a car with the big bell shaped hat on )

I may be totally wrong so dont qote me on it !

Quoted: I see the bobbies with the tall hats and the cops with the checkering on the hats. What the difference? I know in the past the bobbies where un-armed but has the recent situation changed all that because I see the checkered hat guys with weapons all the time. many thanks from your brothers in the states

Clayo's right on this.
If you're out on foot then you wear the tall hat (it's tradition and the tourists love it), but if you're in a vehicle or likely to be, then you wear the flat hats (caps).  Daft really, as cops take their caps off when sitting in the car anyway, but it takes up less room on the parcel shelf, I suppose.

All the English, and I believe the Welsh, forces wear the tall hats and have checkering in the caps. It's dark blue and white checks, unless they are City of London Police (the City Police) who wear a red and white band, not to be confused with the London Metropolitan Police (the Met).

As the firearms units arrive in ARVs (armed response vehicles) they wear the caps.

In Scotland and Ulster they don't have the tall hats, just the caps, unless they're trying to be hard, then like England and Wales they wear baseball caps, usually with the checks or POLICE written on so they're not confused with the bad guys with guns.

What was the original purpose of the big bell shaped hat? Was it like the same reason why the Roman soldiers had crests on their helmet? (to make them taller/more intimidating)

So as they could be identified

COOL!, I learn something new everyday