I think their opposition was even stronger than that and at no point were they ever part of the London regiment ORBAT at all.
This is a great read about the Inns of Court OTC, for they remained an OTC with a cavalry and infantry companies and not a conventional Battalion structure, - Page 41 is a fascinating insight into the way that they recruited pre-war.
https://archive.org/stream/innsofcou...ge/40/mode/2up
The 1911 Army List shows the London Regt's 26 Bns on page 546. The Inns of Court are on the next page as an Indpt unit in their own right.
https://archive.org/stream/hartsannu...ondon+regiment
The HAC remain an Indpt Artillery unit on page 243.