As far as I'm aware, the first police units were to be clad in rifle green and armed (a subsidiary duty being dealing with any naughty French invasion), but I believe disquiet over Peterloo etc., and rich people fearing government lackies, put the kybosh on it.
I suppose a continuation of the militia doing policing, at least in rural areas, could see a situation similar to on the Continent.
The RIC and DMP kept the rifle, for obvious reasons.
The "Gendarmerie" of Britain was the Militia, who were home service regulars whose duties included maintenance of order. The government planning figure was that 50,000 men in arms were necessary to keep Britain under control, and 25,000 in Ireland.
In peacetime, the majority of these men were drawn from the regular Army. However, if mobilised for war, the militia would be called up to replace them. As police forces spread across the country, the militia became freed of even this duty, so that in 1855, a force of militia was available for detachment to the Med (and the Army recruited a lot of regulars from them), and ultimately in 1900, formed militia brigades were deployed to both relieve British regulars for the Boer War, but also deployed directly to the treatre of war.