Low-paid workers were hit the hardest by such job insecurity, as the figure rose to 50% for workers who earn below the real living wage of £9.90 per hour (based on a 37.5-hour working week), and £11.05 for those living in London.
Those polled included cleaners, couriers and NHS staff.
The short notice is not just bad for workers, argued Katherine Chapman, director of the LWF, but also bad for business.
Speaking to HR magazine, she said: "If businesses want to build a resilient, motivated and healthy workforce, secure, guaranteed working hours are essential.
"We’re calling on employers to join those who have already stepped up during this crisis and commit to provide workers with Living Hours – secure, guaranteed hours and notice of shift patterns – alongside a real living wage."
Of the 2,000 adults across the UK surveyed by the LWF, 21% had their shifts cancelled unexpectedly, and 88% said that they were not compensated for their full rate of pay in the event of a cancellation.
Workers with insecure timetables were subjected to a further insecurity premium for everyday services, with 17% of people who had short shift-notice periods paying higher childcare costs, and 27% of the same group paying higher travel costs.
These expenses add extra burdens to those in an already stressful line of work, Chapman said.
She added: "At a time of record increases in the cost of living, this is a particularly tough time for those in insecure work."
The research also highlighted disparity between those above and below the living wage threshold.
The survey found that 50% of those earning below the living wage received less than a week’s notice when being called into work, compared to 28% of those earning above.
A third (33%) of workers earning under the living wage had shifts cancelled unexpectedly in the past year, as opposed to 18% of workers paid at or above the living wage.
“Unless the flexibility of variable hours working genuinely works for individuals as well as their employer, workers’ wellbeing, job satisfaction and performance will suffer and they will stay only as long as it takes to find a better job,” added Ben Willmott, head of public policy at the CIPD.