Jeremy Corbyn was elected as Labour leader on a radical programme of ideas that represented an acute departure from other recent leaders of the party.

In a matter of days, however, many of those proposals have been pared back, reversed or dumped after opposition from colleagues and trade unions. Mr Corbyn says any such compromises are the result of his decision to respect the democratic will of the party.

But Chuka Umunna, former shadow business secretary, has questioned this, saying: “It is not sustainable for us to have a free vote on everything.”

Below are eight areas where there are serious divisions among Labour members that will have to be resolved before the party adopts its official policy lines.

Mr Corbyn, a pacifist, is a passionate opponent of David Cameron’s plan to join US-led strikes against jihadis in Syria. He believes the action would only complicate a proxy conflict that is already taking place — through the involvement of Iran, Russia and others — via the civil war.

Yet he has already signalled that he will not expend too much political capital on the issue. Instead, he will only try to persuade colleagues to come around to his point of view. Mr Cameron is likely to take the issue to a vote in the Commons in the coming months. Mr Corbyn has signalled that he will allow Labour MPs a free vote on the issue, making it much more likely to be approved in Parliament.

John McDonnell, shadow chancellor, has vowed to reduce the deficit without harming people on low or middle incomes. That means a higher top rate of income tax, changes to inheritance tax and — probably — more taxes on property along the lines of Ed Miliband’s proposed mansion tax. He has also claimed much more money can be raised by a crackdown on tax avoidance and evasion.

That has unnerved some Blairite MPs, who believe an overt crusade against the wealthy could deter investment in the UK. They also have misgivings about his claim that tens of billions of pounds could be raised by reducing what he calls “corporate welfare” — tax perks designed to stimulate business investment.

Mr Corbyn is committed to a nuclear-free world and is the vice-chair of the Campaign for Nuclear Disarmament. As such, he would be expected to use the leadership to bring about his life-long ambition of ridding Britain of nuclear weapons.

Once again, however, he has realised the limits of his power after proposals for a vote on Trident renewal at the annual Labour conference were shelved. The unions and some shadow cabinet members — including Hilary Benn, shadow foreign secretary — had issued stark warnings to Mr Corbyn against proposing to scrap the nuclear deterrent.

One union general secretary boasted that he had achieved his desire for “fudge on the menu” over the issue. The Labour leader still hopes to persuade colleagues against the £20bn project but they may not be whipped in next year’s Commons vote on the issue.

Mr Corbyn is determined to scrap the welfare cap, brought in by the Conservatives to limit the benefits received by a single household in any year.

Yet he has already run into conflict with his own shadow work and pensions secretary, Owen Smith. Mr Smith had said Labour was only opposed to plans to reduce that cap from £26,000 to £20,000 — or £23,000 in London. It would be “foolhardy” for Labour to set itself “unthinkingly” against public opinion, he argued.

But his boss stepped in to say that he wanted to get rid of the “devastating” cap altogether, calling it responsible for “social cleansing” in his Islington North constituency.

During the summer Mr Corbyn struck an equivocal note on Britain’s membership of the EU: he would not support the In campaign if David Cameron tried to weaken workers’ rights. That was the same position as the unions who backed his campaign for the leadership.

In 1975 he was among many left-wingers who voted for Britain to leave Europe — but since becoming Labour leader he has been forced by senior colleagues into an emphatically europhile position. Within days he was bounced into vowing that Labour would fight to keep Britain in the EU. Membership was a way of imposing tougher regulations and a new tax on the City of London, he said.

He had been put under pressure by Mr Benn, Tom Watson, deputy leader and Angela Eagle, shadow business secretary.

Labour members, like the Conservatives, are all over the place when it comes to one of the biggest infrastructure decisions facing the UK.

Large numbers of MPs are in favour of the third runway at Heathrow, on which Mr Cameron is due to make a decision before Christmas. Mr Corbyn is instinctively opposed to the project on environmental grounds, as is Sadiq Khan, the party’s London mayoral candidate.

John McDonnell, shadow chancellor, has campaigned vociferously against it. But he said at a fringe event this week that there would be a “democratic decision” by the party. Even if colleagues voted to back the runway he would not resign, he said — citing the “new politics” under the new regime.

Mr Corbyn is deeply opposed to nuclear power and told the environmental organisation Greenpeace during the summer election campaign that he would not support new nuclear power stations.

The government has promised subsidies to back the development of a new reactor at Hinkley Point in Somerset, with an investment decision expected from its French and Chinese investors this autumn. Lisa Nandy, the new shadow energy secretary, has criticised the price that the government has promised for new energy produced at Hinkley.

Ms Nandy said bill payers would have to pay “over the odds” for decades because of the “bad deal”, contrasting it with cuts to renewable subsidies. Yet she also said that she supported nuclear power in general, unlike the leader of her party.

Patrick McLoughlin, the transport secretary, has warned that a Corbyn prime ministership would “throw into jeopardy” the High Speed 2 rail link from London to the north — another long-term project requiring cross-party support.

Mr Corbyn voted against HS2 in 2013. However, his opposition appears to have evaporated in recent weeks. This summer, he wrote a draft speech opposing the project — but when he delivered it, all references to the line had disappeared.

Mr Corbyn recently told the Financial Times it was too late to halt the first section of the route from London to Birmingham and he would not stop the second leg to Leeds and Manchester.