How can Kipps afford a nanny ?

there was no minimum wage back then, so the nanny would have been cheap.

He's middle-class, probably gets a decent salary and has middle-class parents.

If he has financial trouble, the funeral costs and the nanny's wages might be the main reasons. When the wife was alive he was probably doing okay.

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Blood of Thrones - proceeds to Action Cancer:
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A middle-class widower would never have brought up children without a nanny. The money would have been found, by grandparents, godparents etc if his solicitor's salary couldn't meet the expense.