Theresa May has drawn on her childhood memories of growing up in an Oxfordshire vicarage to emphasise her Christian values, which she says “can and must bring us together” over Brexit.

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In an Easter message posted on YouTube, the prime minister calls for British people to show compassion and a sense of community and citizenship, as well as tolerance of other religions, to meet the challenges and divisions caused by the decision to leave the EU.

“Easter is a moment to reflect, and an important time for Christians and others to gather together with families and friends,” May, who is the daughter of a Church of England clergyman, says in the three-minute video.

“This year, after a period of intense debate over the right future for our country, there is a sense that people are coming together and uniting behind the opportunities that lie ahead. For at heart, this country is one great union of people and nations with a proud history and a bright future. And as we face the opportunities ahead – the opportunities that stem from our decision to leave the EU, and embrace the world – our shared interests, our shared ambitions and, above all, our shared values can and must bring us together.”

Reacting to the message, Alastair Campbell, who famously said when working for Tony Blair that “we don’t do God”, suggested May should tread carefully when linking her faith to the political challenges facing the country. “I think even vicars’ daughters should be a little wary of allying their politics to their faith,” he said. “She does not exactly say if God had a vote he would have voted Leave, but she gets closer to it than she should. If she really thinks she is leading a united country full of hope ... I suggest she gets out more.”

Campbell, who is now editor-at-large of the pro-EU weekly newspaper the New European, added: “I don’t think I have ever known Britain more divided. As for her talk of compassion, community, citizenship and obligations to one another, she has taken an axe to those with regard to Britain’s relations to the rest of the world, and plenty of her domestic agenda points in the opposite direction.”

May has stepped up references to her faith in recent months. Recently she lambasted Cadbury’s and the National Trust for supposedly downgrading the word “Easter” on packaging and promotional material. Describing the move as “ridiculous”, she emphasised her dual qualification for passing comment: “I’m not just a vicar’s daughter, I’m a member of the National Trust as well.”

In December, she told the House of Commons: “Our Christian heritage is something we can all be proud of.” In a newspaper interview the same month, she said: “I am a practising member of the Church of England and so forth – that lies behind what I do.” But she stressed that religious tolerance and freedom of speech in the UK need to be safeguarded, adding: “We must continue to ensure that people feel able to speak about their faith, and that absolutely includes their faith in Christ.”

In his own Easter message, Labour leader Jeremy Corbyn said: “We hear painful stories every day, of homelessness, poverty or crisis in our health service – or across the world, of the devastating consequences of war and conflict … It would be easy to retreat into our private lives because the challenges seem overwhelming, or allow ourselves to be divided and blame others. But we need to respond to these problems head on, through action and support for social justice, peace and reconciliation. Those principles are at the heart of Christianity. And Christians throughout the world will this weekend be remembering Jesus’s example of love and sacrifice, and the Easter message of redemption and peace.”

Keith Porteous-Wood of the National Secular Society said: “There can be few countries, if any, where religious expression is as free as in Britain. Perhaps Mrs May’s anxiety about Christians feeling constrained in speaking out is frustration that, in our multi-religious and less religious society, such messages increasingly fall on deaf ears.”

Nick Spencer, author of The Mighty and the Almighty: How Political Leaders Do God, said May’s message appeared to be “motivated by a fear of division”. Linda Woodhead, professor of sociology of religion at Lancaster University, said May’s message was one of “civic religion, rather than orthodox Christian faith”.