The campaign for a referendum on the final Brexit deal has been boosted by a record £1m donation, amid growing public concern that Britain will leave the EU without any agreement.

The multimillionaire Julian Dunkerton, who co-founded the Superdry fashion label, said he was making the donation to the People’s Vote campaign because he saw a “genuine chance to turn this around”. He claimed that, if Brexit had happened 20 years earlier, his brand would never have been a success.

The donation will fund a polling blitz that organisers hope will inject critical momentum into their campaign. Those backing a new public vote face a race against time before Britain ceases to be an EU member after March next year.

An Opinium poll for the Observer has found that 40% now believe it is most likely that the UK will leave in next March without a deal – up sharply from 31% last month. One in five (22%) think Britain will leave with a deal, while 16% think Britain will not leave the EU in March.

Campaigners for a public vote are now planning what is described as one of the “biggest polling operations ever undertaken in UK politics”, examining support for a referendum on the final Brexit deal in different parts of the country and among specific sections of the population.

The most recent polling suggests that 45% of voters want the electorate to have a say on the final Brexit deal, with 34% opposed.

However, serious issues remain over how a second vote could be achieved, whether there is enough time to hold it and what question voters should be asked. Both the Tory and Labour leaderships oppose the idea.

Some senior ministers fear that there is no Commons majority for Theresa May’s proposed Brexit deal, unveiled to her ministers at a meeting at her Chequers retreat earlier this summer and resulting in the resignations of the Brexit secretary David Davis and Boris Johnson. Many MPs and donors are expecting Johnson, the former foreign secretary, to make a pitch for the leadership, while hard Brexiters are drawing up their own preferred Brexit deal.

“We are on the road to misery,” said one senior minister. “[Hard Brexiters] will kill all but ‘no deal’. The Commons won’t vote for that – ministers won’t – so it will all collapse. It could be truly dreadful.”

The government is preparing to release details this week of its planning for a no-deal outcome. Insiders claim that far more work has taken place than assumed, with £4bn allocated by the Treasury to allow for the outcome.

On Thursday, the government will publish the first tranche in a series of technical notices, mapping out the plan for dozens of sectors should no deal be reached. Dominic Raab, the Brexit secretary, will meet the EU’s chief negotiator, Michel Barnier, and will make a speech on the threat of a no-deal Brexit.

“Securing a deal is still by far the most likely outcome, but we want to make sure that we clearly set out the steps that people, businesses and public services need to take in the unlikely event that we don’t reach an agreement,” said Raab.

“It’s the responsible thing for any government to do, to mitigate the risks and make sure the UK is ready to make a success of Brexit.”

Dunkerton, aged 53, left Superdry earlier this year after seeing it expand to more than 500 retail outlets. He told the Observer: “If Brexit had happened 20 years earlier, Superdry would never have become the global success that it did. We would have struggled to cope with negotiating customs and tariffs. Perhaps even more importantly, Europe was our staging post because inside the single market we had no fear of opening a store in France, Germany, Belgium or anywhere else.

“I’m putting some of my money behind the People’s Vote campaign because we have a genuine chance to turn this around. I’ve got a good instinct for when a mood is going to change and we’re in one of those moments now. It’s becoming clear there is no vision for Brexit and the politicians have made a mess of it. Increasingly, the public knows that Brexit is going to be a disaster. Maybe they just need to be given that little bit of hope that comes when they see how opinion is moving.

“I will be paying for one of the most detailed polling exercises ever undertaken by a campaign so that more and more people have the confidence to demand the democratic right for their voice to be heard – to get a People’s Vote on any Brexit deal or the outcome of these negotiations.”

Meanwhile, analysts have discovered that a Brexit skills shortage is already brewing, with employer investment in training per employee falling by 27% in the last decade.

Analysis of government figures by the Institute for Public Policy Research found that, despite a record level of skills shortages, employers’ investment in training is low and falling. There were 226,000 “skills shortage vacancies” last year, compared with just 91,000 in 2011.

With Brexit expected to exacerbate the problem, the analysis shows investment per employee has fallen by 27% in real terms between 2007 and 2017. Total employer investment in training has been cut by £3.7bn in real terms over that period.