Business leaders today called for urgent action to make it easier for firms.
It comes after a foundry revealed it had lost orders and was facing higher costs.
Netherton Foundry in Highley said it had taken on extra staff just to deal with paperwork that needs to be completed as part of new regulations.
Shropshire Chamber of Commerce today said it had received reports of a number of businesses being unable to continue trading with Europe at the same level they had before.
The Chamber said the local situation is a reflection of the national British Chamber of Commerce survey, which found that half of exporters were facing difficulties in adapting to the changes in the trade of goods.
Ruth Ross, Shropshire Chamber’s director of business, said it was unacceptable for businesses not to be able to trade at the same level as they had before.
She said: “There are many other companies, just like Netherton Foundry, who will not be finding it easy to adapt to the new rules.
“We have seen reports in recent days from other Shropshire companies suggesting they are finding it difficult to continue trading with the EU at the same level as they were doing before Brexit. Clearly this is unacceptable.
“When asked about the specific difficulties businesses were facing, commonly cited concerns from the survey included increased administration, costs, delays, and confusion about what rules to follow.
“We are calling on the Government to work with the Chamber network to identify the most significant blockages for businesses, and act swiftly to publish plans for resolving them.”
A spokesman for the foundry, which sells cookware, said: "Increased documentation means that we need to use higher paid staff to complete shipping details.”
The firm said it is losing orders due to new duty and customs arrangements, as well as time – and therefore money – spent resolving European customers' enquiries.
The business said the cost of implementing new shipping arrangements and delivery charges on its website is another burden.
The spokesman added: “A small business like ours does not have the resources to deal with all the extra work."
There have been several other firms which have been vocal about the disruption which has hit their businesses since the changes came into force.
Businessman Michael Harte, of Telford-based food firm Bridge Cheese, said empty shelves and disrupted supply chains would continue unless the food and drink sector gets greater support.
Mr Harte said even companies that stockpiled ahead of the December 31 end of transition deadline were struggling, with cashflow tied up in stock that cannot be delivered to customers or held up at ports.
Shrewsbury-based natural food company Purition said it has currently been forced to stop trading with Europe because of Brexit issues.
Meanwhile a firm specialising in the importing and exporting of agricultural products said it has been hit by delays at ports since new Brexit trade rules came into force.
Shrewsbury-based Gwaza Ltd only managed to ship five out of about 120 planned orders to customers in Europe in January, with the remaining stuck at the ports.
One of the suggestions from the BCC, which is backed by the Shropshire Chamber team, is the creation of tax credits allowing firms to offset their spending on adaptation to the new UK-EU requirements against their tax bills.
The BCC also wants the Government to look at key areas of the new relationship and work with EU partners on easements to minimise ‘unhelpful burdens’, including on aspects of Rules of Origin and VAT.