Define branch line! If it is a single track branch or secondary line then signalling will be provided at and on the approach to crossing loops or junctions. You would not usually find intermediate signals mid-section, unlike other parts of the world. A simple single track branch line might not have any signalling at all beyond its junction point, if one train working is in operation, other than a fixed distant approaching the terminus. Other secondary lines operate under remote arrangements, with points indicators and stop boards with the driver required to obtain a token or staff from a machine and permission to proceed. In some locations RETB (radio tokens) are used and the Cambrian Lines in Wales now use the sophisticated ERTMS signalling system to control train movement.
Cheripok has given good insight into colour light signals. Broadly speaking on (say) a 100 MPH main line under 4 aspect signalling these will be spaced around 1200 yards or 3/4 mile apart. That gives a braking distance of around a mile and a half from sighting the double yellow, to coming to a stand at the red. However in more lightly trafficked areas, colour light signals were simply installed to approximate where old manual signalboxes were taken out (the Devon banks between Tavistock Jn and Totnes is an example of this) and the block sections are several miles long. In this case you would get a colour light distant signal at sufficient braking distance from the next "home" or stop colour light signal.