Hi,
There were probably a few British rifles during the flint era with octagon to round or tapered round barrels but the vast majority had swamped octagon barrels because the British tended to emulate German traditions when it involved rifles. The military Baker rifle is an example with a round barrel but the stock is clearly similar to Jaeger rifles. Below is a photo of 4 British rifles from 1779-1782. They are all full stocked, octagon barrels, and show strong Germanic style.
Notice also, they all have flat faced locks, which was almost universal on high quality guns after 1765 or so. Mike is probably right about when hooked breeches, usually called standing breeches, became popular with British makers. Standing breeches go hand in hand with using barrel keys rather than pins.
Big Bubba, the barrel on my rifles was from Charlie Burton. It is 54 caliber, 32" long, and 1 1/16" at the breech with a straight taper to about 15/16" at the muzzle. I don't remember the twist but the rifling was square bottomed and deep. I installed a custom made chambered breech that I designed machined from a block of 4140 steel.
dave