That is an interesting question - would developing london further cause the abandonment of valuable infrastructure already constructed elsewhere?
Luckily we can study the data as it stands - the ONS provides
subnational breakdowns of population projections out to 2039.
If we strip out only 'all ages' data for each local authority area, and calculate the percentage population change between 2014-2039.
You can then sort the dataset by population increase, only 11 local authority areas have projected negative population growth.
Those are:
Barrow-in-Furness
Isles of Scilly
Copeland
Richmondshire
Hyndburn
Cumbria
Blackburn with Darwen
Allerdale
Blackpool
Redcar And Cleveland
South Lakeland
However, Burnley also shows zero population growth.
Of these, only five shows a bigger than 2.0% population reduction, which leaves:
Barrow-in-Furness
Isles of Scilly
Copeland
Richmondshire
Hyndburn
The Isles of Scilly has a reduction of ~10%, but only has a population of 2,000 to start with and isn't really relevant to this discussion.
The remaining areas only have a population in 2039 of 256,000 people and will show a decrease of 15,000 people relative to 2014.
So even at current rates the growth of London is hardly going to lead to a dystopian abandoned north.
Is that a bad thing?
If what we know about the dynamism of large urban areas is true, imagine the wonders that would come out of such a conglomeration.