“Tax the rich, jail the fossil-fuel executives and deliver the Green New Deal” – so chants the Labour-supporting economist Grace Blakeley, one of the more moderate voices on social media. It’s catching.

Jeremy Corbyn was also talking tough this week. He identified some of the capitalist criminals Labour is coming for, including Sir Jim Ratcliffe of Ineos. Though it’s not clear under what law the polluting plutocrats could be prosecuted.

So, is this class war in the UK? Are we on the road to Venezuela? Whatever the polls say, a Labour victory this Christmas is quite possible with Nigel Farage’s Brexit Party now splitting the Tory vote. There is a powerful mood for change in Britain. But what would a Labour government actually look like?

We have never had such an avowedly radical Prime Minister – not even in 1945, when Labour was led by a small “c” conservative, Clement Attlee. However, Labour reality would be rather different from the rhetoric. Burrow into Labour’s policies, and what emerges looks more like reheated social democracy, circa1974, than a Bolshevik revolution.

For a start, we can largely ignore the issue that divided the party so bitterly in recent times: nuclear weapons. Jeremy Corbyn may be a lifelong member of CND, but Labour is no longer a unilateralist party. Its 2017 manifesto committed a Labour government to renewing Trident almost indefinitely.

But Corbyn will still enter Number 10 with a raft of left-wing policies, from seizing corporate assets to abolishing private schools as well as taxing the rich until the pips squeak. However, many of the headline policies will never make it to first reading, let alone the statute book.

Abolishing schools like Eton would involve lengthy court action, not least from faith schools and the home school movement, who might also be affected. Labour is more likely to confine its assault on educational privilege to axeing tax reliefs worth about £1.5 billion

Similarly, seizing 10% of the shares of companies with more than 250 employees would be fiercely resisted in the courts by shareholders. They have deep pockets. I suspect Labour would confine itself to increasing corporate taxes, ending zero-hours contracts and restoring trades union rights – all of which are eminently doable.

Indeed, looking behind the radical rhetoric, much of Labour’s policy agenda is surprisingly modest, viewed from Scotland. Measures like free personal care, abolishing university tuition fees, childcare for three and four-year-olds, scrapping the right to buy, lifting the benefits cap and the bedroom tax – these are all achievable.

Indeed, the Scottish Parliament has already achieved them, bar the welfare cap. Nicola Sturgeon will no doubt remind the Labour leader of this repeatedly in coming weeks.

Nationalisation is a policy that used to be seen as “loony left” but is no longer. Taking rail into public ownership shouldn’t be too much of a problem, since Network Rail, which owns the track and signalling, is already in public hands. The service franchises could be replaced as they come up for renewal, without needing to hand billions in compensation to Virgin and the rest.

Water (in England) and energy would pose greater problems, not least because most of our energy companies are foreign-owned – often, ironically, by state-owned bodies. But with a good wind it should be possible for Labour to find a way. Public attitudes to public ownership of utilities have changed out of all recognition since the 1990s.

Similarly, there is broad public support for Labour’s Green New Deal. A majority of voters agrees there is a climate emergency. Though they may not agree with the measures needed to tackle it.

Labour is not going the full Extinction Rebellion route of making Britain zero carbon by 2025. But its own policy, passed at conference, is still pretty radical. It commits a Labour government to making Britain zero carbon by 2030. That’s only five years longer.

We are talking about the most radical change to our lifestyles since the industrial revolution. Labour’s policy would mean decarbonising transport, home heating and agriculture in a decade. Millions of cars would have to be scrapped along with millions of home boilers. Air travel would all but cease.

Labour promises a huge investment in renewable industries to compensate, but that is unlikely to replace the jobs lost in the car industry, oil and gas, road haulage and retail.

So expect the Green New Deal to become somewhat lighter green in government. There is likely to be a rift between the Thunberg-supporting “de-growthers” and Labour MPs, who traditionally see economic growth as the best way to address poverty and inequality.

However, Britain already has a rather good record on eliminating greenhouse emissions, and this will continue, albeit with the 2030 target reduced to 60% net zero.

In sum, Labour offers a practical social democratic programme which could be very attractive to voters, especially younger ones. However there is one very big problem: Brexit.

Labour is committed to negotiating a new Withdrawal Deal to replace Boris Johnson’s (even though Brussels has said it will not reopen it) and to putting this to another Brexit referendum. This will consume a vast amount of political capital and will surely dominate the first year of a Labour government.

Corbyn wants to reintroduce the customs union and Brussels would probably agree to that. But Labour also wants close regulatory alignment with the European Single Market, which the EU 27 would probably reject. If Britain wants to be in the single market, it will have to join the single market, probably via the European Economic Area, along with Norway.

Labour could go along with that in the end, since it wants friction-free access to the EU markets. Single market membership would solve the Irish border problem, for sure.

But it would also mean Britain continuing to contribute to the EU Budget, while having no say over decisions taken by Brussels. Customs union membership requires oversight by the European Court of Justice, which will displease many.

But that wouldn’t be the main problem. If Labour got this wonderful deal, including workers’ rights and environmental standards, and got it through Parliament (and if Labour is a minority government that could be difficult), would it really then campaign against it in the confirmatory referendum?

Interviewers have largely stopped asking this question, because they never get an answer, but Europe remains a huge question mark hanging over Labour’s government agenda.

Labour is still a Brexit party, though you wouldn’t know it to listen to most MPs. Many figures in the party are closet Brexiteers, like Jeremy Corbyn himself. Others are openly pro-Brexit, like the party chairman Ian Lavery and the MPs who voted for Boris Johnson’s deal.

Equally dedicated Remainers – mostly Blairites and supporters of the deputy leader Tom Watson – would fight back, insisting that Labour effectively promised to back Remain in the General Election. Brexit wrangling could delay the confirmatory referendum and divide the party, just as it split the Tories.

Corbyn’s enemies will ignite further division by condemning him as anti-Semitic. It will take immense powers of leadership to prevent a Labour government being halted in its radical tracks by Brexit.

The question for voters is: does Jeremy Corbyn possess it?