It's been recorded by the shanty group Monkey's Orphan on their CD More Monkey Business!. The online notes say:

From the singing of an ex shipmate of Shanty Jack, G.L, in the Tugs in the 1970s. He said this version was sung in the Royal Marines, including the final shouted responses. The third verse Jack stole from another R.N. song and spliced it in to add a bit of length because he only got two verses from G.L. and every time he sang it people wanted more! Aladdin is possibly a derivative of the shanty "Pretoria" which was a South African song shanghaied by sailors. Cyril Tawney has a R.N. version in his book "Grey Funnel Lines."