Libertarian-Elizabeth giving orders to Philip? Are you talking about like, the Order of the Garter, Grand Cross of Bath, that sort of thing? She can bestow that on anyone she wants.
I imagine Phil would be a Knight of the Garter.
That link gives exactly what I was thinking of (in the sub-links to and Precedence I and Precedence II which seem to answer the OP in mind-numbing detail. While trying to recover from the misplacement of my book last night I found Debrett’s site, but never thought of Burke’s.