S&P said the the referendum result could lead to “a deterioration of the UK’s economic performance, including its large financial services sector”.
Earlier the pound plunged to a 31-year low against the dollar, and UK markets closed lower for a second day.
S&P had been the only major agency to maintain a AAA rating for the UK.
On Friday, Moody’s cut the UK’s credit rating outlook to negative.
A rating downgrade can affect how much it costs governments to borrow money in the international financial markets. In theory, a high credit rating means a lower interest rate (and vice versa).