A no-deal Brexit could cause the UK to lose half a million jobs and nearly £50bn in investment by 2030, according to an economic forecast commissioned by the mayor of London, Sadiq Khan.

The report, which models five possible scenarios for leaving the EU ranging from a near-status-quo situation to leaving on World Trade Organisation terms without any transition agreement, warns that the worst option could be a “lost decade” of economic slump.

Quick Guide What are Brexit options now? Four scenarios Show Staying in the single market and customs union The UK could sign up to all the EU’s rules and regulations, staying in the single market – which provides free movement of goods, services and people – and the customs union, in which EU members agree tariffs on external states. Freedom of movement would continue and the UK would keep paying into the Brussels pot. We would continue to have unfettered access to EU trade, but the pledge to “take back control” of laws, borders and money would not have been fulfilled. This is an unlikely outcome and one that may be possible only by reversing the Brexit decision, after a second referendum or election. The Norway model Britain could follow Norway, which is in the single market, is subject to freedom of movement rules and pays a fee to Brussels – but is outside the customs union. That combination would tie Britain to EU regulations but allow it to sign trade deals of its own. A “Norway-minus” deal is more likely. That would see the UK leave the single market and customs union and end free movement of people. But Britain would align its rules and regulations with Brussels, hoping this would allow a greater degree of market access. The UK would still be subject to EU rules. The Canada deal A comprehensive trade deal like the one handed to Canada would help British traders, as it would lower or eliminate tariffs. But there would be little on offer for the UK services industry. It is a bad outcome for financial services. Such a deal would leave Britain free to diverge from EU rules and regulations but that in turn would lead to border checks and the rise of other “non-tariff barriers” to trade. It would leave Britain free to forge new trade deals with other nations. Many in Brussels see this as a likely outcome, based on Theresa May’s direction so far. No deal Britain leaves with no trade deal, meaning that all trade is governed by World Trade Organization rules. Tariffs would be high, queues at the border long and the Irish border issue severe. In the short term, British aircraft might be unable to fly to some European destinations. The UK would quickly need to establish bilateral agreements to deal with the consequences, but the country would be free to take whatever future direction it wishes. It may need to deregulate to attract international business – a very different future and a lot of disruption.

The analysis by Cambridge Econometrics predicts that a no-deal Brexit could shed as many as 87,000 jobs in London alone, with the capital’s economic output 2% lower in 2030 than what would be expected under a soft Brexit.

“If the government continue to mishandle the negotiations we could be heading for a lost decade of lower growth and lower employment,” Khan said. “The analysis concludes that the harder the Brexit we end up with, the bigger the potential impact on jobs, growth and living standards.”

The Labour mayor was a strong supporter of the remain campaign and has since vigorously argued for the UK to stay in the EU’s single market and customs union, or for London to be granted its own deal, especially on maintaining rules on banking and financial services.

The report concludes that while every Brexit outcome would harm the UK economy, “the harder the Brexit, the more severe the economic damage could be”.

It says that while London would suffer in a no-deal departure, it would fare better than the rest of the UK – nationally, the most damaging sort of Brexit would see economic output up to 3.3% lower in 2030 than would be the case with the status quo, which would widen inequalities.

Speaking on BBC Radio 4’s Today programme, Khan said: “London does least worst, because we have a higher concentration of high value jobs, we are more resilient, more able to recover from economic shock, which could lead to the inequalities between London and the country getting worse … Whatever scenario we look at when it comes to leaving the EU, the inequalities between London and the south-east and the country widen, not narrow.”

Khan commissioned the report after the Brexit secretary, David Davis, told MPs he had not, as long believed, ordered central government impact assessments into the potential economic effects of Brexit.

Khan said it was “astonishing” that Theresa May’s government had failed to do any analyses.

He said: “I’ve released these impact assessments because the British people and our businesses have a right to know the likely impact of the various options the government are considering on their lives and personal finances.

“This new analysis shows why the government should now change its approach and negotiate a deal that enables us to remain in both the single market and the customs union.”

The worst of the five scenarios modelled – departure in March 2019 with no deal or transition arrangements – would lead to 482,000 fewer jobs across the entire UK and a loss of £46.8bn in investment by 2030, the report says.

With no arrangement for the service sector, financial and professional services would be worst affected, shedding nearly 120,000 jobs, with 92,000 fewer in science and technology and 43,000 fewer in construction.

The report says that even a softer option, such as the UK remaining in the single market but leaving the customs union after a transition period, could end up with 176,000 fewer jobs by 2030 and a loss of £20bn in investment.

Khan and the report’s authors stressed that the figures were indicative, and that a huge number of factors could affect what happened, but that it was the first time such an analysis had been undertaken.