The coat was blue. That's the whole argument, really — the army wore red, so these men would not; and the hat was a top hat, civilian, the sort a clerk might own. No sabre. A wooden truncheon under the coat and a wooden rattle to make a noise with, which is about as much force as you can carry without looking like a soldier.
Peel had spent years being told by Parliament that a standing police was a French idea and the beginning of the end of English liberty, so when the first of them walked out in 1829 the uniform was doing a fair amount of persuading on his behalf. As it happens the headquarters backed onto a yard off Whitehall, which is how a Scottish street name ended up meaning something else entirely. The rattles stayed in use for decades before anyone thought of a whistle.
Those top hats were reinforced, which sounds like it's for the head. It was so a constable could stand on his hat to see over a wall.
The rattles went out in the 1880s in favour of the whistle, which carried a good deal further and had nothing to jam — a rattle with a cracked spring or a swollen wooden tongue just clicks. Marguerite, the whistles were made in Birmingham by Hudson, and much the same pattern stayed in service for a century.