Speaking outside 10
Downing Street, he said"fresh leadership" was needed.
The PM had urged the
country to vote Remain but was defeated by 52% to 48% despite Scotland, London
and Northern Ireland backing staying in.
UKIP leader Nigel
Farage hailed it as the UK's "independence day", while Boris Johnson
said the result would not mean "pulling up the drawbridge".
Scottish First
Minister Nicola Sturgeon said she was "absolutely determined" to keep
Scotland in the EU so a second Scottish independence referendum was now
"highly likely".
German chancellor
Angela Merkel expressed "great regret" at the outcome, and EU chiefs
said they expected the UK to begin negotiations to leave "as soon as
possible, however painful that process may be".
But Boris Johnson, the
ex-London mayor and public face of Vote Leave who is now a front-runner to be
next prime minister, said there was "no need for haste" about
severing the UK's ties.