I have seen an illustration of the Naval Brigade parading through London after returning from the Egyptian campaign. At their head the officers are carrying two flags. One appears to be an unadorned Union Flag. The other is slightly obscured. It may be a White Ensign (it has a small Union Flag in the corner), yet I cannot see a red cross. The lack of a cross may mean it is an Ensign of another colour, yet by this period the Royal Navy had ceased to use any but the White Ensign, so it might just be an oversight by the artist.
I do, however, have no idea if such flags were ever taken into action.