We are actually given a very clear description of the family's economic condition towards the beginning of the story. It seems to be clear that the family is not actually badly off, but through the bad management of their money and the need that they have to keep up appearances through consumption of wealth means that they are always in want. Note what the text tells us:
Although they lived in style, they felt always an anxiety in the house. There was never enough money. The mother had a small income, and the father had a small income, but not nearly enough for the social position which they had to keep up... There was always the grinding sense of the shortage of money, though the style was always kept up.
Apparently, Lawrence based this story on a friend (though whether she remained a friend after reading this story is not known) called Lady Cynthia Asquith, who married somebody who did not have enough money and always felt herself to be short of wealth. The suggestion is, however, that if they had not felt it so important to keep up their "social position," they would have had enough to live very comfortably.