Britain must remain part of the European Union to protect its economic interests but a post-crisis Europe must not turn into a rigid bloc with the power to hurt those on the periphery, British Prime Minister David Cameron said on Monday.

Cameron asked in a foreign policy speech to the Lord Mayor of London's banquet: What kind of Europe do we actually want?.

One with the flexibility of a network, not the rigidity of a bloc, whose institutions help by connecting and strengthening its members to thrive in a vibrant world, rather than holding them back, he said.

The eurosceptic Conservative leader, prime minister in a coalition government with the smaller and europhile Liberal Democrats, wants to maintain Britain's influence in Europe while also urging further integration in the euro zone as part of a solution to the debt crisis.

The government is worried, however, that a closer-knit euro zone could isolate non-euro nations in the EU and form a powerful voting bloc which could damage the interests of countries such as Britain and Sweden.

Although a more closely integrated euro zone, which potentially votes as one on Europe-wide issues, could have damaging long-term consequences for Britain, Cameron is urging the euro zone in that direction because the alternative - a break up of the monetary union - would be disastrous for Britain's fragile economy.

Some European countries are calling for deeper euro zone fiscal integration to help deal with the financial crisis.

Some on the right of Cameron's party have called for Britain to leave the European Union or at least to use the euro zone crisis as an opportunity to claw back powers from Brussels.

Cameron faced a rebellion by more than a quarter of his members of parliament last month who defied him to demand a referendum on EU membership. The episode had echoes of infighting over Europe tore apart the Conservative government in the 1980s and 1990s.

Leaving the EU is not in our national interest, Cameron said, according to a copy of his speech released in advance by his office. Outside, we would end up like Norway, subject to every rule for the Single Market made in Brussels but unable to shape those rules.

And believe me: if we weren't in there helping write the rules they would be written without us - the biggest supporter of open markets and free trade - and we wouldn't like the outcome.

However, Cameron said the EU must find a way to get its economies expanding again. Unless we all get a grip on growth the European Union will remain an organisation in peril representing a continent in trouble.

TRADE AND POLITICS

Cameron, citing figures showing European countries accounting for half of UK exports, said Britain also needed to focus on building stronger ties elsewhere to improve its prospects in an increasingly competitive global environment.

If we are to earn our living in the rest of the world, we also need to forge stronger relationships with countries like Brazil, Russia, India, China, Turkey, Nigeria and South Africa, he said.

Cameron said he would not shy away from seeking business, even in countries with poor human rights and political records.

In dealing with other countries, their politics matter. But when the politics are troubling the answer isn't to deal with the politics and put the trade on hold, he said.

We must be bold enough to try and deal with the politics and the trade at the same time. We should always be a champion of human rights - and we should address our differences candidly. But we should not allow them to define and limit the whole relationship.

(Reporting by Matt Falloon)