I've been looking at the zonal single fares for NR within London
zones, and they are all less than £4 except for zones 1 - 6.

However, in the section on exceptions, it says "... those
circumstances where fares for use on some National Rail services are
set by London Underground. This generally applies where there is a
choice of London Underground and National Rail services on joint or
parallel routes. On these routes, the fare for the journey will
continue to be the appropriate London Underground fare for the journey
being made."

Does this mean that a single, for example, from Barking to West Ham on
NR is £4 instead of the usual £1.90 for an NR zone 3 - 4 single?