Good choice as they are both next door to each other, hell you can walk right through one into the other, while there, jump next door to the Victoria And Albert Design Museum which is just across the road.
Great Museum, lots of haunting exhibits which reminds you of the human cost of war (I'm talking most about the cast replicia of a Hirshoma victim....)
Umm no it's not, the British Museum is in the vicinty of Tottenham Court Road, while the Portrait Gallery is just behind Trafalger Square.....