Hi Andrew ,
Interestingly enough I have been to the NMM on a few occasions in recent years but did not notice this ( presumably because I did not have any interest in edged weopans until recently ) . From what I remember the collection was made up mainly of "Nautical" ceremonial blades ( I think there was a short Japanese sword as well ) . I 'll try to go there again next time I'm in London .
Britain is littered with war spoils from Burma especially cannons ( I think almost every castle I've been to has a Burmese cannon in its collection - perhaps an exaggeration I know but I've seen at least 6 in 6 different places ) and bells .
The dha in your picture is a working man's all purpose dha ( in Burmese it would be in the Dha-ma or chopper category despite its length ) which would have been used for splitting wood as well as splitting other things

. I used to have a picture of the common ( non uniformed and not part of the standing army ) Burmese soldier circa 18th century carrying one of these .
If it came without scabbard and sometimes common soldiery may well have had to do without it would be termed
dha-hlut literally meaning loose dha (
dha-lwe means dha worn over shoulder ).