Strict legislation prescribes that Freedoms of The City are to be accorded only to individuals. Units thus are given (only) freedom to fly their Colours and march with fixed bayonets etc. but City of Westminster acknowledges the distinction is fine.
The belief is that the following have that right:
4th Battalion, The Royal Green Jackets (as was) 5th December 1985
HMS WESTMINSTER 11th December 2005
Seemingly, A Company London Scottish maintain they were given this right pre-1965 (when the current City of Westminster was formed). However, nothing can be found to support the claim.