The average UK family’s disposable income reached £160 a week in June for the first time in 2013 but weak wage growth continued to put pressure on consumers’ spending, according to Asda.

The figure from the Asda Income Tracker is flat on the same month last year but down £5 a week from its peak of £165 in February 2010.

Weak wage growth was a key factor, up just 1% in the year to May – one of the smallest year-on-year rises on record.

Average pay excluding bonuses was up 1% in the three months to May. This was a third of the rate of essential item inflation (3%) and only marginally better than the 0.8% growth – an all-time low – seen in the three months to March.

Asda said that, had it not been for the rise in the income tax-free allowance in April – from £8,105 to £9,440 – household disposable income would have fallen even further, by an additional £5 a week.

Across the regions, there was good news for households in the North West, which witnessed a £5 increase in disposable income year-on-year. At the other end of the scale, households in Northern Ireland continue to see a decline in disposable income of £4 over the same period.

Asda chief executive Andy Clarke said: “Although customers don’t seem to be any better off than they were this time last year, a positive rise in retail sales indicates a return to cautious spending.

“It is unlikely that consumer confidence will be fully restored until we see a significant improvement in family finances, but the good news is that the cash in our customer’s pockets appears to be stabilising.”

He added: “With the recent heatwave and two British sporting victories in the bag, consumer spirits are high, hopefully leading to a brighter outlook for July.”