They mean the City of London. They capitalised the C and everything, it's a thing.

> I was walking in central London .... there are no trees in central London (the City).

It makes me wonder whether they know which bit is actually the City.

later on:

> Sure, you have a small/big park here and there

What big park is there within the City? The whole of the City is smaller than Hyde Park (including Kensington Gardens).