Leotech wrote:...The horn button seems to put the white to earth when pressed.
which is how it should be
try earthing the horn terminal that the white wire goes into straight to earth, with the ights on.
if the horn works then problem is likely to be with the switch.
if it still doesn't [but does with the lights off], issue will be with the brown feed, either on the junction board, with the ignition switch [if you have one] or again back at the light switch.
maybe check the light switch is working as it should be with a multimeter
and are the lights bright enough...?