LONDON (Reuters) - Ratings agency Moody's will downgrade the credit rating outlook for major British banks to "negative" on Tuesday because of the fallout from the vote to leave the European Union, Sky News reported, citing sources.

A Sky News reporter said "a number of big UK lenders" had been told by Moody's that their credit rating outlook would shift to negative from stable or positive.

Fitch and Standard & Poor's cut Britain's sovereign credit ratings earlier on Monday, judging the vote to leave the EU will hurt the economy.

(Reporting by Andy Bruce)