Meanwhile the fog and darkness thickened so, that people ran about with flaring links, proffering their services to go before horses in carriages, and conduct them on their way. The ancient tower of a church, whose gruff old bell was always peeping slily down at Scrooge out of a Gothic window in the wall, became invisible, and struck the hours and quarters in the clouds, (Chapter 1)
There are two environments that you might possibly be referring to, the physical environment of the weather and the social environment of the state of the city. If it is the weather environment you ask about, the affect it has is to provide the mood, the atmosphere, of the tale. The frozen cold fog is dense when the story opens (though people still come and go with good cheer and good will). Cratchit sits in terrible numbing cold. Scrooge does too but it doesn't bother him. Later, the weather environment enhances Scrooge's loneliness and solitary isolation in his large, dark, cold house. Later still, when Scrooge is visited by the Spirits, this external environments instills inner fear and dread inspired first by Morley and then by the three Spirits.
If it is the social environment and state of the city--Victorian London during the Industrial Revolution--you ask about, it was teeming with displaced farm laborers who had left quiet villages to come to the city. They met overcrowding and inadequate housing with no privacy, no old friends, only strangers and horrible factory working conditions. There was dirt, squalor, hunger, disease, destitution, exhaustion, poverty, want and care at every turn and down every avenue. This has an affect on the tale by forming part of the essential premise of the story: destitution and want must be driven off by human warmth and generosity of both pocketbook and heart. Tiny Tim and Crachit form the major plank of the story premise but a parallel plank is provided by the representatives of charity in the early passages of the story.
“it is more than usually desirable that we should make some slight provision for the Poor and destitute, who suffer greatly at the present time. Many thousands are in want of common necessaries; hundreds of thousands are in want of common comforts, sir.”
“Are there no prisons?” asked Scrooge.
“Plenty of prisons,” said the gentleman, laying down the pen again.
“And the Union workhouses?” demanded Scrooge. “Are they still in operation?”
“They are. Still,” returned the gentleman, “I wish I could say they were not.”
“The Treadmill and the Poor Law are in full vigour, then?” said Scrooge.
“Both very busy, sir.”
“Oh! I was afraid, from what you said at first, that something had occurred to stop them in their useful course,” said Scrooge. “I’m very glad to hear it.” (Chapter 1)