Some 46% of households said they would struggle to cope if their outgoings increased by this level, according to research from Halifax.
People aged in their 40s and 50s were found to be the most stretched, with 18% of people in these age groups saying their budgets would buckle if they had to find another £24 a month.
Two-fifths of households said they expect their general financial situation to worsen in the next 12 months and pessimism was highest among those in their 50s, with 56% saying this.
Halifax suggested that the middle generation, which often has children living at home, has been hardest hit by household bill increases.
On average, 26% of households reported higher spending on fuel and energy bills in the last 12 months, rising to 29% for those in their 40s and 50s.
While 8% of households reported an increase in food costs, this rose to 9% for people aged in their 40s.
Anthony Warrington director, personal current accounts at Halifax, said: "Those in their 40s and 50s are most likely to have family living at home, which means their food and energy bills are likely to be higher."