Tom Stoppard suggested recently that Brexit was too big a subject to be easily dramatised. But the National has had the bold idea of collating interviews from around the UK, carried out after the referendum, to discover what people really feel about their country. The resulting 80-minute show, jointly credited to the poet laureate, Carol Ann Duffy, and Rufus Norris, is never dull but tends to confirm what we already knew: that the referendum has revealed just how fractious and divided we are as a nation.

The evening starts with Britannia (Penny Layden) convening a meeting with representatives of Caledonia, Cymru, Northern Ireland, south-west England, the north-east and the east Midlands.

The actors who speak for their specific territory hold up photos of the interviewees whose testimony we will hear. In much the best part of the evening, we then get six arias from highly articulate individuals. The class divide surfaces in Scotland where a former state school pupil resents the privileged enclave of neighbouring private school Fettes.

A former police officer from Wales talks bitterly of a tenant who claims more in benefits than she herself ever earned. An east Midlands resident reminds us that Britain is not the land of milk and honey of which many immigrants dream.

I had hoped for more such extended monologues. But, divided up into separate subjects such as Europe, patriotism, immigration, the vote and its aftermath, the evening becomes increasingly fragmented.

Angry voices are raised as the actors bark out single-sentence opinions. Britannia tries to moderate the discussion and Layden voices the views of politicians: she does a particularly good Boris Johnson, carving the air with his right hand as he utters his surreal fatuities. There are also shafts of humour as when a bewildered voice tells us that “we heard on the news that terrorists are coming into Wiltshire but I haven’t seen any”. But the overriding impression is of a country filled with a simmering resentment.

This makes it all the more surprising that Britannia finally refers to “changing, feisty, funny, generous islands”. Generosity is hardly the quality that emerges from these raging vox pops. By deliberately excluding London and the south-east, the production also does scant justice to the remain cause. And there is one question I longed to hear asked: how did people get the information that informed their vote? I was struck by how often people’s fears, on a variety of subjects from the EU dictating the shape of bananas to the notion that asylum seekers are sending money home to “murderers and rapists”, seem to reflect the prejudices of the anti-European press.

Norris’s staging is lively and the six actors who speak for the people – Seema Bowri, Cavan Clarke, Laura Elphinstone, Adam Ewan, Stuart McQuarrie and Christian Patterson – do a perfectly good job. But, however well-intentioned, the show offers little in the way of fresh information or insights. We already knew that the EU had become a scapegoat for popular discontent and that there are serious fissures between, and within, the UK’s separate parts. Even though the show ends with a plea for “good leadership”, it offers no hint from where, in our disunited kingdom, that might conceivably come.

• At the National’s Dorfman stage until 22 March. Box office: 020 7452 3000. Then touring the UK.