Scots will no longer be British if their country votes to leave the United Kingdom, Labour leader Ed Miliband has warned in a keynote speech on national identity.

Miliband insisted that leaving the union would mean that Scottish people would lose their British identity – challenging the argument put forward by the Scottish Nationalists, who have insisted that Scottish people would continue to be British in a geographical sense.

Alex Salmond, leader of the Scottish National party, has drawn a parallel with the way Swedish or Norwegian people can also consider themselves Scandinavian.

Miliband chose to make his speech between the Queen's diamond jubilee celebrations and the opening of Euro 2012, calling for more debate and pride in being English as part of the multiple national identities that British people can have.

The speech was scheduled to chime with a summer of celebrations in which people around the UK are celebrating under different national flags: the union flag for the jubilee, the Olympics and the Paralympics, and the cross of Saint George for Euro 2012.

It was also a direct challenge to the campaign for Scottish independence led by Salmond, which is gathering momentum north of the border.

Miliband struck at the emotional heart of the debate in telling a questioner: "People can be Scottish and British, it's OK. And if they feel primarily Scottish that's fine too. But if they leave the UK they won't be British any more: it stands to reason."

The difference was that Scotland and England were jointly British because they were part of a political union, said Miliband.

He also continued to rule out demands for an English parliament to mirror the powers of the Scottish parliament and the Welsh assembly, saying there was no public appetite for "more politicians" and he would prefer to see stronger local government instead. Labour was also deterred by the "bloody nose" it got over its proposals for regional assemblies, he said.

The Labour leader denied there was a "West Lothian question" – the issue over Scottish and Welsh legislatures ruling on policies such as education with no interference from Westminster, while votes on the same subjects in the House of Commons include Scottish and Welsh MPs. "The threat doesn't hold because there was a decision [in Westminster] made to devolve those issues to the Scottish parliament and Welsh assembly," he said.

Speaking to an audience at the Royal Festival Hall in London, Miliband said: "While there is romanticism on the left about Welsh identity [and] Scottish identity, English identity has tended to be a closed book of late. People have been nervous that it would undermine the UK, but also because it connected to a nationalism that left people ill at ease."

He continued: "Now more than ever, as we make the case for the United Kingdom, we must talk about England … If we stay silent, the case for the United Kingdom in England will go by default."