Perhaps the key difference between grumpy and mardy is that the former involves more anger and the latter more self-pity. However, in an almost bipolar way, the mardy arse will tend to be someone who mood-swings from mardy to lary – from surly/resentful to surly/aggressive – often when alcohol has been added as a catalyst.
The term is a coarser and therefore more emphatic version of mardy bum (the 'bum' in this sense referring to the buttocks, not a beggar or hobo, and 'arse' being a less polite word than 'bum'). It may be heard in the same Derbyshire, South Yorkshire, Nottinghamshire, Leicestershire zone of the English East Midlands where mardy is commonplace, though principally the city of Leicester.
Got beat at darts, and buggered off home in a mood.
Oh, he always was a mardy arse!