Marzy wrote:
I thought it was unlikely, however there must of been times when they were in England on the same day so to speak?
David,
I don't think that would have been possible either. It was just over a year after Endeavour returned home that Cook set out again on his second voyage in July 1772. Nelson, coincidentally, returned home from his 'educational' voyage on the Mary Ann under Maurice Suckling's old shipmate John Rathbone, in the same month. It's hardly likely therefore that there would have been any possibility of a meeting, even under Maurice Suckling's guidance, or of Nelson joining either Cook's second voyage, or similarly the third of 1776–9. By that stage Suckling had secured Nelson in his chosen profession, and as Tony mentions, would he have been that interested in any case having already been part of one expedition? He had taken to the fighting side of the RN, rather than the exploratory one!
There would actually appear to have been a much closer connection between Cook and Nelson, than through Bligh. This was none other Mrs Cook, then of course a widow, who apparently was a frequent visitor to Merton where she had a relative living nearby. I'm sure the Nelsons would want to have met her (we can speculate that Emma and Nelson would probably have had different reasons) and during which visits she must have spoken a great deal about her husband. (One wonders how much she actually knew about the voyages themselves, as I would imagine Cook perhaps didn't tell her much about the details which Nelson would certainly have been interested in.) She must have been a remarkable lady, surviving not only her husband but, sadly, all of her children – and I believe dying just a short while before Victoria came to the throne in 1837.
I think you can tell I've been doing a little light reading!

Btw, I have just been watching the third in the new mini series about Cook, currently being broadcast here in Sweden. I'm finding it very good.