It's important to differentiate between services that are self contained entirely, with no track connection to the main lines, and services which are run as self contained but share connections.
Everywhere on the network, barring certain unforseen circumstances, is connected to everywhere else. That is the virtue of a national network. Any unit could in theory be dragged everywhere else.
However, some services run as self contained shuttles. The Bromley North, Stourbridge Town, Looe and St Ives lines all run self contained during normal service, but share connection.
Other examples which theoretically could run without interference from the outside network are the Far North Line, by virtue of separate platforms at Inverness, and Merseyrail similarly with separate platforms at Ellesmere Port and Chester.