Business leaders have called on Amber Rudd to urgently publish an investigation into Britain’s reliance on EU workers, arguing that delays would be “catastrophic” for business.

They say the report, which is not due until September, just days before a Brexit deal is expected to be sealed with the EU, will come too late for businesses desperately trying to plan their futures post-Brexit.

“The government’s refusal to publish its findings until two days before the UK’s scheduled departure from the EU could be catastrophic for the continuity of the supply chain,” said James Hookham, deputy chief executive of the Freight Transport Association (FTA), which represents cargo owners ranging from Tesco and John Lewis to Honda.

The FTA along with other business leaders is calling for an interim report or the employment data to be released “as soon as possible” to start “an honest debate about how reliant Britain has become on EU workers”.

Their concerns echo warnings from businesses that they are already seeing a shortage of EU workers. On Monday it emerged that farmers in the Channel Islands fear that their next crop of Jersey Royal potatoes could be affected by a shortage of Polish workers who have previously harvested them. Around 1,000 foreign workers are needed to pick the potatoes in Jersey each year.

The home secretary commissioned the report from the Migration Advisory Commission last summer in the face of fierce industry opposition to a clampdown on immigration post-Brexit.

The Recruitment & Employment Confederation (REC) called on the government to grasp “the urgency” of getting the official data on EU citizens into the public domain.

“Employers have to look at contingency and the worst case scenario is that companies decide to invest elsewhere or move part of their business out of the country altogether where they will be able to get the workers,” said Tom Hadley, director of policy at REC.

The National Farmers’ Union has called for the publication of an interim report.

“The more clarity we can get for EU workers coming in and out of the country the better,” said Tom Keen, Brexit adviser at the NFU.

He said it was not just important to allow fruit and vegetable farmers to hire seasonal workers, but also to give security to workers who come for a few years and then return home.

Hadley described the report “as a bit late in the day” and said he feared immigration policies would prioritise skilled workers, not people working in the fields “picking potatoes or flowers”.

Employers ranging from the coffee shop chain Pret a Manger to the NHS have complained they cannot recruit British workers or are losing foreign EU staff because of Brexit.

The FTA says logistics is the “lifeblood” of industry and very vulnerable to Brexit.

The sector employs 310,000 EU workers, about 12% of the workforce, including 35,000 drivers of vans, forklift trucks and large goods vehicles.

“If those EU workers are to be denied access to work as the UK leaves the EU, their employers need to know now so that plans can be made now, not with only two days’ notice,” said Hookham.

Pete Taylor, operations director at Encore Personnel Services, said numbers of EU citizens were already declining. Some of the agencies who acted as middlemen for his recruitment in places such as Latvia, Poland and Romania had already gone out of business because of Brexit.

He places up to 4,500 unskilled temporary workers a week into car plants in the Midlands, including BMW and Jaguar Land Rover, and into the large logistics warehouses dotted around the motorways.

“It is absolutely vital we see this report without delay and see the statistics. It was bad enough before Brexit. Even if we had British workers there wouldn’t be enough of them to meet demand,” said Taylor.

• This article was amended on 25 January 2018. Pete Taylor is operations director, not manager, at Encore Personnel Services, and Honda is a previous not current client. This has been corrected.