The depth of cabinet divisions over Europe has been laid bare as the education secretary, Nicky Morgan, warns that a UK exit would cut the country off from the rest of the world and limit the freedom of young people to study and find jobs in the European Union.

Writing in Sunday’s Observer, Morgan hits back at anti-EU cabinet colleagues who are preparing to campaign for “Brexit”, saying the next generation should not have to live in a country in which their prospects and opportunities “end at our shores”.

In her additional role as minister for women, she says the EU has been at the forefront of campaigns to end exploitative practices such as female genital mutilation and forced marriages, and has been a champion of women’s issues.

Her intervention, backed by Downing Street, is an opening salvo by pro-EU ministers at the very top of government after the hardline Eurosceptic Chris Grayling, leader of the House of Commons, was first out of the blocks on 13 January in arguing that staying in the EU as it is currently run and organised would be disastrous for the UK. While David Cameron is said to be “relaxed” about Grayling’s remarks, Downing Street is keen not to allow Eurosceptics to make the running in the debate ahead of the in-out referendum, which now looks likely to be held in the summer or autumn.

Morgan’s aides denied that the education secretary was jumping the gun by campaigning to stay in the EU before Cameron’s renegotiation of the UK’s membership had concluded. However, her remarks reflect growing tensions between her cabinet colleagues, and the impatience of senior ministers from both camps after the prime minister said they would be free to take up pro or anti-EU positions once the process was over.

Months of tortuous talks now appear to be moving towards a conclusion, with EU diplomats increasingly confident that a deal can be done in the middle of next month that would allow the prime minister to call a referendum as early as June. On Friday, the president of the European commission, Jean-Claude Juncker, said he was “quite sure” an agreement would be reached by then.

EU sources say a deal now looks possible on Cameron’s most hotly contested demand – that EU migrants should have to wait for four years before receiving any in-work benefits in the UK.

While all the other 27 EU nations have warned they cannot accept the proposal, Cameron has said he would be prepared to look at other ideas that would have the same effect of reducing “pull factors” that attract EU citizens to the UK.

Morgan focuses on the interests of young people, saying she does not want her own son to grow up in a country “that puts a limit on his ambition”, and implies that multinational companies would find the UK less attractive if it were not in the EU.

“I want him to be free to join thousands of British students studying at colleges and universities in Germany, France and the rest of Europe; I want him to be able work for a company that doesn’t just have offices in England, but in Dublin, Lisbon and Stockholm – joining one of the thousands of businesses that operate in Britain and Europe; and I want him to broaden his horizons – able to travel freely and safely across Europe along with millions of other Britons who visit the continent every year.”

She adds: “Why do I say all this? Because it goes to the heart of the negotiations the prime minister is leading in Europe, negotiations which won’t just define our future role in Europe, but the kind of Britain our children will grow up into.

“I think all of us agree what we don’t want that Britain to be: anti-competitive with more laws made overseas and with people travelling here for the benefits on offer rather than to pay their way. But we also don’t want our children to inherit a Britain cut off from the world, where their prospects are limited and their opportunities end at our shores.”

Conservative MP Damian Green, a board member of Britain Stronger in Europe, said it was important that the positive case was heard from as many Tories as possible. “This shows the wide range of Conservative voices who see the positive aspects of EU membership. It is a myth that the default Conservative position is anti-EU. Pragmatic Conservatives always look for the practical advantages for people in any institution, and that is what we should be doing with the EU.” Morgan says that most women she meets approach the debate on Europe with the interests of their families uppermost in their minds. “They want to know: does being in Europe make it easier or harder for my daughter to get a job? Does being in Europe make it more or less likely my son will be able to afford to buy a house? Does being in Europe mean my family will be safer from a growing terrorist threat?

“The prime minister’s renegotiation goes to the heart of these concerns, ensuring that Britain gets the benefits of the increased security, clout and prosperity that EU membership can bring, but recasting our relationship so that we no longer face the regulations that make us less competitive, the laws that creep and the policies that encourage people to travel to Britain for the wrong reasons. If he’s successful, as I am confident that he will be, then the answer to those questions will be yes.”