Business leaders have rallied to support Theresa May’s Brexit deal, even as an independent study showed that the prime minister’s agreement meant the UK stood to lose £100bn a year by 2030 in reduced trade and income.

Executives in the City of London warned MPs to vote for the deal negotiated by the prime minister to avoid a no-deal Brexit that would harm the UK economy.

TheCityUK, which represents banks and insurers in the Square Mile, said parliament had “a straight choice” between the agreement hammered out in Brussels and a no-deal Brexit, “which offers only higher risk, costs and disruption”.

Miles Celic, the organisation’s boss, said: “The focus must now be on securing the withdrawal agreement and the transition period it brings – which is critical for our industry and many others. There is much still to be negotiated to define the future relationship. The sooner that can get started, the better.”

His warning echoed those of industry bodies and small business groups, which have become nervous in recent weeks that No10 would fail to overcome the hurdles towards securing a withdrawal agreement.

The Institute of Directors, which has found in polls of its members that they split 50:50 over proposals for a second referendum, said they all objected to an outcome that leaves Britain with no deal.

“The deal the EU approved today provokes a wide range of reactions across the political spectrum, and indeed among business leaders, but the steer from our members is that avoiding no deal must be the main priority,” said Stephen Martin, the director general.

Helen Dickinson, chief executive of the British Retail Consortium, said: “It is now up to parliament to ensure that we can have a transition period from 29 March and avoid a chaotic no-deal Brexit for consumers.”

Business concerns about the failure to secure an agreement came as a study found that a no-deal Brexit would cost the UK £140bn a year by 2030 and the trade deal planned by May following a two-year transition period would cost £100bn a year.

Analysis by the National Institute for Economic and Social Research found that the May deal would mean the UK’s national income (GDP) would fall by 3.9% – or £100bn annually – and total trade between the UK and the EU would fall by 46%. Tax revenue would fall by 1.5% – 2%, the equivalent of £18bn-£23bn less to spend on public services at today’s prices.

NIESR said: “If the government’s proposed Brexit deal is implemented so that the UK leaves the EU customs union and single market in 2021, then by 2030 GDP will be around 4% lower than it would have been had the UK stayed in the EU.

“This is largely because higher impediments to services trade make it less attractive to sell services from the UK. This discourages investment in the UK and ultimately means that UK workers are less productive than they would have been if the UK had stayed in the EU,” it added.

The cross-party Peoples’s Vote organisation said: “Although the proposed UK deal envisages no tariffs or quantitative restrictions, the UK would not enjoy Norway’s full access to the EU’s single market through the European Economic Area or Switzerland’s comprehensive regulatory alignment through bilateral agreements that allow free movement of labour.”

The report also modelled alternative Brexit outcomes against staying in the EU. A relationship based on the UK remaining in a customs union beyond the transition period, possibly through invoking the so-called Irish “backstop”, would still mean a hit to GDP of 2.8%, the equivalent of £70bn a year.

Another scenario, favoured by some Brexit supporters, of an “orderly no deal” departure from the EU would reduce GDP by 5.5%, or £140bn a year.