This was signalled by the seasonally adjusted UK Household Finance Index (HFI) posting below the 50.0 no-change mark at 44.3, down from 44.8 in the previous month.
The degree to which finances deteriorated was the second-strongest since January, behind only that seen in May.
Retail employees gave the bleakest assessment. There were worries about job security, although income from employment rose at a faster pace. Prices pressures meanwhile eased to the weakest in four months.
Current financial strain intensified, while workplace activity fell for first time in over four years, leading to greater job insecurities, but income from employment rose at a record pace. Meanwhile, some 56 per cent of households expect the Bank of England to lower the base rate, compared to just eight per cent in mid-June.
Philip Leake, economist at Markit, which compiles the survey, said: "Markit’s latest HFI survey suggests that the Brexit vote has badly affected households’ views on their finances. With future prospects clouded by uncertainty, July data pointed to the worst financial outlook in two-and-a-half years. "Household concerns also intensified as workplace activity fell for the first time since May 2012, with employers awaiting a clearer picture following the ‘Brexit’ vote.
"Worries about the future are at least being offset by some better news on wages and interest rates. "Pay growth picked up to a survey-record high, indicating that the National Living Wage is feeding through to rising incomes. "Meanwhile, July data signalled a huge shift in interest rate expectations following the EU referendum. The minutes from last week’s Bank of England policy meeting implied a strong chance of a rate cut in August, and this is reflected by 56 per cent of respondents predicting a fall in the base rate, up from eight per cent in June and contrasting with a rate hike which had been largely predicted up until the ‘Brexit’ vote."