British Officers AND Other Ranks attached to the Gurkhas generally carry the Kukri on their webbing (I was certainly almost encouraged to) and are often presented with a Kukri on their departure from the unit.
This is for the Corps', the RGR might be different.
The kukri is only worn on no 2 dress, 1s and ceremonials (pipers etc) by Gurkhas. Obviously the Officers (Britap and Gurtap) carry swords, and the British ORs don't carry the kukris or wear the distinctive Gurkha hat.
It's worth noting that there is NO formal dress regs for British ORs attached to Gurkha units. So a certain lee way is thus available.