So, just for context, Scotland is a bit more than half the size of England, meaning England has gone from ~2x as densely populated to ~5x.

Geography accounts for part: on the whole Scotland is more hilly, less fertile and with a harsher climate. Just have a look at this map for example. Far fewer areas of Scotland were suitable for the agricultural revolution that helped kick-off rapid population growth in England. Scotland still has quite a different pattern of land use and ownership.

Likewise I think the industrial revolution kicked off more strongly south of the border, perhaps because of greater wealth or the location of resources (especially coal & iron).

Scotland began the 19th century poorer than England and has continued that way. That alone may account for much of the widening gap in population, as it encouraged faster population growth in England (natural and immigration) while Scotland had higher emigration (much of it to England). I think that Scotland, Wales and Ireland all share similarities in terms of emigration, though of course none to quite the same extent as Ireland. Scotland also has a notably lower life expectancy than England, although I don't know how much of an impact that has on the population figures.