The German chancellor Angela Merkel has issued an emphatic plea for Britain to stay in the European Union, saying the EU needs Britain to help develop the single market and to improve competitiveness.

At an event for European students in Berlin on Tuesday night, Merkel said the EU must work closer together on political as well as economic matters, specifically in developing a European defence policy.

"You can still have many dreams," she told a student who asked if she had a "European dream" to restore trust in those who had lost trust in the EU. "I think that, for example, we are going to have to work a lot closer together on defence policy," she added, going on to outline areas which needed attention.

"We have a few EU countries which are not in Nato, which raises lots of question marks. We are doubling, even tripling up on some resources," she said, acknowledging Germany was often the roadblock on decisions about deploying troops to a conflict zone because German law requires the parliament to vote on such matters.

The meeting's moderator, Financial Times journalist Quentin Peel, made reference to the venue, the Neues Museum redesigned by British architect David Chipperfield. It was a shame, he mused, that there were not more British "architects" involved in shaping Europe's future.

But Merkel insisted Britain was still a key player in Europe. Britain is "very serious" about the single market, she said.

And when it came to discussions around thorny issues such as "service directives" or making the working time directive more flexible, "it wasn't Britain which is holding things up", she said. "Britain is essential and also more pro-European than some other countries," when the EU is negotiating on a global scale, for example on climate protection, she said.

She added: "We want to have Great Britain in the European Union. We need Britain, by the way. I want to say this emphatically, because Britain has always given us strong orientation in matters of competitiveness and freedom and in the development of the single European market."

The chancellor said she bristled at the stereotyping of Europeans. "There are lazy and hardworking Germans," she said. "I always intervene when I hear people saying things like, well, the Germans are in favour of federalism and the French are centralistic so no wonder, etc. It's exactly the sort of thing we need to get over."

She also said it was not true that Germany was a model to its neighbours in all respects. One of Merkel's favourite words during the euro crisis has been "hausaufgaben", the German for homework, which she uses to urge errant EU members to do as they are told and carry out reforms.

But, she said: "There are lots of situations where we have not done our homework. So if I look at the French family politics, I can say that the work life balance there was better 20 years ago than ours is now.

"We're still having the conversation about whether you can be a good parent if your child doesn't eat their lunch at home. Other countries laugh at us and say what's going on there then?"

She added: "You only need to look in Germany at how long it takes to build a stretch of road or a station to see that we are clearly not top of the class in Europe in all respects."