Three in five (58%) said their employer would stop supporting them beyond this period, while a quarter (24%) have no sick pay to fall back on.
But just 7% of those surveyed have an income protection policy, despite a quarter (25%) buying pet insurance which costs a similar amount.
Tom Conner, director at Drewberry, said: “The survey has highlighted just how financially vulnerable the UK workforce is to ill health and disability.
“Clearly if you have limited employer sick pay and savings and no insurance a family would need to rely on benefits, which are only a very basic safety net.
“Unless a family has other income streams to help them they will need to dramatically slash their expenditure.
“That could mean taking drastic action to reduce debts such as selling the family home.”
The majority (55%) of people's savings would last less than three months.
Of the people surveyed one in five (19%) has been off work for more than three months in the past.
Conner added: “We always suggest income protection as the most important type of insurance to protect against this type of worst case scenario.
“It replaces your income tax-free when you’re too ill to work and pays out until you’re well enough to work again or until the policy ends.
“You can choose for it to pay out until you retire so you are protected for the rest of your working life.”