Probably refers to the National Portrait Gallery in London. Walters (302) says museums and galleries have a reputation of keeping large stocks of paintings in storage. Goodman (142) says portraits are sometimes given to the Crown as equivalent payment for death duties. Such acquisitions may end up gracing the dimly-lit corridors of civil service buildings. Shepherd (263) reports having heard "Smithsonian" substituted for "Nation" in some productions. That may seem out of place, but at least American audiences would understand the joke. Turnbull (294) mentions that after the Art Council of England refused the D'Oyly Carte Opera Company a grant, Kenneth Sandford, playing Despard, changed the line to: "I will give them all to the Arts Council "-- a well-deserved jab that received enthusiastic audience acclaim.

I will give them all to the Nation, and nobody shall ever look upon their faces again
Act I