Shantying was not used in either navy mainly because it wasn't necessary and you wouldn't be able to hear anyone sing anyway. Discipline was so strict and all jobs were done to perfection immediately on order. Also there were plenty of hands to the pumps as it were. There simply wasn't time for anyone to organise anyone to sing, or any need. There was so much bustle, activity and noise on a man-o-war a shanty would have been pointless.

Merchant ships in contrast were usually short on manpower(The Navy pressed most of them)and needed the extra pull/push the shanty gave. Many of the crew were ill-disciplined and green and the shanty at least kept them together in time.

The only references to shantying on board RN vessels are a few vague references on board revenue cutters in the early 19th century.

The above info I have gleaned from reliable sources in old magazines lime 'Mariner's Mirror'