British motorists face a 10% rise in the cost of their annual car service and repair bills if the UK leaves the EU without a trade deal, an industry body has warned.

The UK’s collective car repair bill could rise by more than £2bn due to tariffs and other barriers arising from a hard Brexit, according to a report published by the Society of Motor Manufacturers and Traders (SMMT), which assumes the UK is forced to fall back on World Trade Organisation (WTO) rules.

The prediction comes after warnings from various industries about the impact on their sectors of a hard Brexit.

They have ranged from the UK nuclear industry highlighting the “cliff edge” faced by not replacing the existing European nuclear treaty, Euratom, to farmers warning that the price of British strawberries could rise by more than one-third if the UK cannot ensure access to European workers after Brexit.

Speaking about the motor trade, Mike Hawes, the chief executive of SMMT, said: “If we don’t secure a new trading relationship with the EU that is free of tariffs and customs checks, British consumers could face significant increases to their annual car repair bill due to new tariffs and other trade barriers.

“Government must now prioritise an interim arrangement that maintains single market and customs union membership until the right trade deal with the EU is implemented.”

The SMMT’s report said a WTO tariff on imported car parts of between 2.5% and 4.5% would cost the average car owner an extra £21 a year for replacement components.

Meanwhile, quotas, subsidies, customs delays and regulatory barriers could add an additional £49, adding up to a £2.14bn rise in the UK’s collective car maintenance bill, the trade body said.

Theresa May has previously said “no deal is better than a bad deal” when it comes to the terms of Britain’s departure from the EU, suggesting the prime minister believed that falling back on the default position of WTO rules in the absence of a trade deal with the EU is a credible alternative.

However, the Guardian reported in February that leaving the EU without a trade deal would saddle British exporters with more than £6bn a year in new tariffs.

The SMMT said: “Some 80% of replacement car parts fitted to British cars are imported, with almost three-quarters of these coming from EU-based suppliers. However, the manufacture of components in the UK is growing, making the risk of tariffs on British products sold in Europe and other key global markets another major concern.”

The report concluded that WTO tariffs on automotive parts exported from the UK could cost the domestic industry up to £3bn in lost revenue, “with a potential impact on future investment and jobs”.

Despite talk of no deal, many Brexit observers believe there has been a softening of the government’s stance since the general election, with increasing talk of the UK negotiating a transitional agreement.

In research published on Sunday, the political consultancy Eurasia Group said: “To clear the air and offer more certainty to business than the government’s current nods and winks, ministers believe that May will make a major speech on Europe in September.

“This will update the government’s policy, including on the transitional period. It would mark a significant retreat from the hard Brexit she would have pursued had she won a majority in the June election.

“Until then, however, uncertainty will likely remain on what the transitional deal might involve. UK ministers have not discussed it in any depth. [Philip] Hammond accepts that the UK will technically leave the EU, and its single market and customs union, in 2019.

“At the same time, he is seeking a solution that in practice implies largely accepting free movement of labour, continued budget payments and the continued adoption of EU laws and the jurisdiction of the European court of justice, hence dubbed a ‘status quo’ transition.”

The SMMT and Eurasia reports were released as economic optimism fell to the lowest level for six months, according to the latest study of business confidence from Lloyds Bank Commercial Banking.

Economic optimism slipped by one percentage point from 18% to 17%, it found.

The negative figures came as overall business confidence remained unchanged at 30% in July, the bank said, just below the long-term average of 32%.

The share of companies reporting higher business confidence decreased by three points to 45%, but this was offset by those reporting lower confidence, which fell by three points to 15%.