Historically, the U.K. had quite pronounced local variations in the styles of some tools, screwdrivers being one.
The first tool shown is clearly a “London pattern” screwdriver, so yes, I’d be guessing British made.
As Farmer J says, “Heart Brand” tools were made by Wynn Timmins and it looks like their logo, I have a pair of pliers around with the same logo.
In this instance I am sure that the tool is a Wynn Timmins as I have seen identical tools so marked. I think my local used tool shop has a couple in stock now.
I suspect that this tool has some age to it, but the steel, the forging, and the grinding on these old tools is usually first class.
The pattern of the blade, although slightly unusual to modern eyes, is even older than the tool, but they are incredibly good to use. I know one local carpenter who has a collection of these that he retains for working with traditional sized slotted screws.