but the fan
instructions state that I can only wire it independently using a
pull-cord switch, or wire it in parallel with the bathroom ligh

thats how you do it then




And does the fan still need to be wired through a double-pole
isolation switch, despite not being wired to the light? Can I just use
a double-pole FCU like Screwfix 16437?

fans are usually wired into the lighting circuit using 3 core cable and
isolated using a fan isolator switch