Not sure how you can describe the City as the 'least democratic' borough (it's not a borough) in the whole country.
Surely, with its 25 wards and an alderman each to represent its residents, it's very democratic indeed, coming much closer to the Swiss model than the rest of the UK.
Not to mention its independence from the crown.
Also, housing 'citizens' outside of the boundary dates back to the 16th century, when there was a huge influx of migrants from the North of England. Of course the City could have chosen to deny the immigrants from Yorkshire access, instead it chose to allow them in and house them where possible.
Keeping many of the public spaces in London (for example Hampstead Heath), offers a nice tax break for the Corporation of London. I don't see how places like Hampstead fall under your category of chucking poor people out of its boundaries?