A blue ensign as the National Museum is a public body. The badge in the fly features a shield with a Union Jack chief, with the cross of St George in the rest of the field. This is inspired by the White ensign, the national flag flown by British navy ships. It is of course topped by a Naval coronet/crown.
A flag variant of the shield could be used as a jack:
The initials of the National Museum of the Royal Navy are on the white field. Although in the case of a jack the civil jack would probably be more appropriate as this is in effect the naval jack (Union Jack) with a white boarder. A variant of the ensign with letters: