The index, which is based on answers to eight questions on job security, business activity, house values and household finances, was at 111.9 in the first three weeks of June, but has fallen 7.6 points to 104.3 since the vote to leave the EU.
It is the lowest level of consumer confidence since May 2013, when the index was at 102.9.
The figures from YouGov and the Centre for Economics and Business Research (Cebr) show that consumer confidence had already fallen between May and June, thanks to homeowners concerns about property prices over the next year, and the levels of business activity at people’s places of work.
Cebr director Scott Corfe said the data showed that households were "highly spooked" by recent developments, and that brexit could lead to a "marked slowdown in the economy" in the near future.
He added: "A recession certainly cannot be ruled out at this point."
A spokesman for the British Retail Consortium said: "Following the EU referendum result, we need certainty at speed. Knowing how the Government intends to implement the referendum result will reassure business and allow consumers to better understand how the next steps impact them and their families and to plan accordingly."