The most common reason for migration has always been economic. In the UK the start of the industrial revolution caused large numbers of people to start moving to the bigger cities and overseas in search of better paid work. So for your ancestor I would look to see what employment he was engaged in, in Greenwich. That might be the answer to your question as to why he moved.
The journey from Dundee to London in the early 1800s may not have been as difficult as you think. Though an overland journey was possible, it was probably more likely that he and his wife went by sea. There were regular shipping services up and down the east coast of Britain, which would enable people to travel from Dundee to London relatively easily, if not in great comfort.
Elwyn
