See: London Scottish (regiment) - Wikipedia for an answer. And: The London Scottish Regiment (Estb. 1859) - London Scottish Regiment
The London Scottish were officially part of the Gordon Highlanders but that really just meant that the Gordon Highlanders provided all the Regular staff during peace time. They provided an Adjutant, a Training Major, a Quartermaster, a Regimental Sergeant Major and a bunch of Sgts, CSgts and WO2s. The London Scottish continued to wear its own colour of kilt and wear its own cap badge. Regards Frank