The Present Situation Index (how consumers feel about the current economic and employment situation) and the Expectations Index (how consumers feel about the economic and employment situation in six months time) also were down in June, the report revealed.
"The fall in confidence in June reflects some weakening sentiment about the economy and jobs, both now and in the future," Fionnuala Earley, Nationwide's chief economist, said.
"Higher interest rates are likely to be a major factor behind this as consumers recognise their impact on the wider economy as well as on their own pockets. Spending confidence ticked up very slightly in June but overall it is significantly lower than this time last year.
"It now seems likely that rates will rise in July with a significant risk of a further increase in the autumn and we expect to see consumers tightening their belts in the months to come," she went on.
The Spending Index rose in June - but Ms Earley described the measure as "very volatile" and said it was easily affected by seasonal variables.
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