David Cameron has used his annual Lord Mayor's Banquet speech to call for fundamental reforms of the EU and reiterated his desire for powers to be transferred away from Brussels and back to Britain.

Calling for powers to "ebb back, instead of flow away", the prime minister castigated the makeup of Brussels, saying: "For too long the EU has tried to make reality fit the instutions. But you can only suceed in the long run if you make the institutions fit the reality."

In a apparent riposte to Europhiles in Britain and to both Angela Merkel and Nicolas Sarkozy, Cameron added: "We sceptics have a vital point. We have a right to ask what the European Union should and shouldn't do and shape it accordingly."

Cameron suggested that some eurozone leaders were viewing the rise of new powers such as Brazil with a sense of "alarm and crisis", adding: "Old assumptions are collapsing. It was said that no exit from the Euro could ever be envisaged, powers would always go one way, to the centre. And now everything is changing."

However Cameron made the case for remaining in the EU, saying leaving would be damaging for Britain.

"European countries account for 50% of our trade," he said. "Leaving the EU is not in our national interest. Outside we would end up like Norway, subject to every rule of the single market, but unable to shape those rules. "

In a speech seriously short on laughs - other than claiming that dressing up for the Banquet made everyone look "like extras in Downton Abbey", Cameron expressed a sense of vindication, suggesting those who thought the operation to remove the old regime in Tripoli were merely "pessimists".

Cameron said that in liberating Libya, "we helped to keep the Arab Spring alive," but revealed that in the past few days the new Libyan authorities have found chemical weapons that were kept from the world.