A Conservative party donor has called for a referendum to be held on the final Brexit deal, amid new warnings about the huge financial costs of leaving the EU without an agreement.

Sir Simon Robertson, the former banker and Rolls-Royce chairman, said that he was “deeply depressed” by the direction of the Brexit debate and believed there should be a chance for a vote on the final deal hammered out with Brussels.

His backing for a second public vote suggests that there is support for the move among senior Tory remainers. However, campaigners only have a narrow window in which to secure it.

“I think it is complete balderdash to say the people have spoken, therefore you can’t go back. The people can speak again – why can’t we have another vote on it,” Robertson told the Observer.

“We had a brilliant deal with Europe. We had an opt-out on ever-closer union, we weren’t in the single currency and we were not in Schengen [the EU’s visa-free travel area]. We had a perfect arrangement. We are now going to end up with one where, at the end of things, we won’t have a final say.

“I’m not saying for a moment that it solves the underlying problem – which is the fact that some people have felt left behind. I think that in many ways, they have.”

We had a perfect arrangement. We are now going to end up with one where we won't have a final say Sir Simon Robertson

However, it comes after Theresa May vehemently ruled out a second referendum, saying she would not “give in” to the demands.

“In the summer of 2016, millions came out to have their say,” the prime minister said. “They trusted that their vote would count; that after years of feeling ignored by politics, their voices would be heard. To ask the question all over again would be a gross betrayal of our democracy – and a betrayal of that trust.”

Meanwhile, industry bodies are still demanding clarity on the Brexit talks. The government has been releasing “technical notices” about a no-deal outcome, but there has been little detail on the overall extra costs involved.

Some carmakers could face added costs of up to £1bn and companies in the food and drink sector could face an extra £60m in costs a year under a no-deal outcome, according to analysis by auditors KPMG. The extra bureaucracy, storage and tariff implications could lead to companies in the clothing sector being hit with as much as £15m in extra costs.

Tariffs on parts being ferried to and from the port of Dover in the car manufacturing cycle will add significantly to companies’ costs. Photograph: Daniel Leal-Olivas/AFP/Getty Images

Bob Jones, director and Brexit customs lead at KPMG, said these high costs were a result of complicated supply chains criss-crossing the English Channel, together with any new administrative and duty burdens.

“Automotive clients that move goods frequently across the EU-UK borders as part of their manufacturing cycles could incur significant new administrative costs and some duties,” he said. “The costs of each part crossing the border can snowball and compound through the supply chain to the point of vehicle manufacture. With duties of 10% on finished vehicles into the EU, and with 40% of UK production headed there, the worst-case ultimate costs for a significant UK automaker could increase by between £500m and £1bn.

“Food and drink industry clients face very significant new tariffs on EU-UK trade because of high common external tariffs on food, as well as high administration costs due to health regulations. Several clients in this sector could see costs rise by up to £60m.”

Meanwhile, a new assessment of the costs incurred as a result of customs checks under a no-deal outcome suggest a £2.5bn bill. The assessment by Andrew Meaney, from the Oxera financial economics consultancy, states: “Our analysis of a no-deal Brexit suggests that, even under conservative assumptions around the increase in vehicles to be checked by member states, the costs to hauliers would amount to £2.5bn. None of this analysis includes the further costs associated with delays on surface transport routes to and from ports and railheads.”

The paper also predicts a “significant increase on consumer expenditure on food overall”. It states that an estimate by supermarkets of a 12% increase in food prices in a no-deal scenario is “likely to be an underestimate if sterling were to devalue against the euro in the event of no deal”.