He described as pessimists those who argue Britain should leave the bloc and say there is no prospect of reforming the EU.
"I think they are wrong ... I think it is possible to change and reform this organisation," Cameron told an investment conference.
Cameron came under renewed pressure from within his Conservative party this week when former finance minister Nigel Lawson said a plan to renegotiate Britain's commitments to the EU, before an expected membership referendum in 2017, was doomed to fail and the country should leave the bloc.
London Mayor Boris Johnson, speaking at the same conference, said the party should rally around Cameron and his plan.
But Johnson, who is believed to harbour ambitions to succeed Cameron as leader of the Conservative party, also said Britain should be ready to "walk away" from the EU if it fails in its renegotiation bid.
"This is not for Britain the existential question it was ... when we joined at the height of the Cold War," Johnson said. "We now live in a globalised economy where the real growth markets are to be found outside the European Union."
Membership of the EU has been a divisive issue for the Conservatives for decades and Cameron hopes the referendum will settle it once and for all. It depends not only on securing more favourable EU membership terms but also on the Conservatives forming Britain's next government after elections in 2015.
But the idea that Britain should cut off ties with Europe in order to increase those with Asia and America was rejected as “ludicrous” by British MEP Graham Watson, the president of the Alliance of Liberals and Democrats for Europe.
“I am not at all convinced that the UK would get as good a deal if it tried to negotiate on its own,” Watson wrote in an opinion piece published by EurActiv. “There is a reason why Obama's State of the Union address did not announce a brand new trade deal with the UK - the idea is almost laughable. A trade deal with the EU, however, is a big banana for the world's biggest economy, worth the investment of political capital.”
Watson also challenged Lawson’s claim that the loss of the EU’s single market would be only marginal for Britain. “The fact is that we export more to the Netherlands than to China, Brazil, Russia and India combined. Almost 90% of small business exporters rely on trade with the EU.”
