Did the fleet flagship sit outside its battle squadron?

Was the Royal Navy fleet flagship normally separate from its battle squadrons?

No. In Royal Navy practice it tended to operate within a squadron; the separate flagship arrangement is associated here with German practice.

Squadron arithmetic changes if a fleet flagship is counted as an additional ship outside the squadrons. That arrangement is associated here with German practice. In Royal Navy usage, the fleet flagship tended to operate within a squadron. Counting an extra flagship therefore does not resolve the proposed British building programme in the way the question suggests.