Morale among small businesses is weaker than a year ago, although stronger than shortly after Prime Minister Theresa May lost her majority in June, according to the survey from retailer Amazon UK and business promotion company Enterprise Nation.
Businesses have been hit by higher raw materials costs due to the fall in the pound since last year's Brexit, and the survey showed firms expect a continued squeeze on revenue over the next year.
However, 73 percent of firms have not delayed business decisions as a result of the Brexit vote. Of those that have, hiring was the main area affected.
Some 42 percent of small businesses surveyed wanted Britain to stay in the European Union, but most want to leave - albeit with little agreement on terms.
Just over a quarter of firms wanted a Canadian-style trade deal with the EU, 13 percent want ties like Switzerland's, while smaller proportions wanted to be part of the European Economic Area trade bloc, a customs union or have no trade deal at all.
Finance minister Philip Hammond told lawmakers on Wednesday that uncertainty about the shape of Britain's future deal with the EU was harming investment and consumer confidence.
The survey was based on replies from 1,031 senior decision makers at small and medium-sized businesses who were polled by market research company YouGov between Aug. 17 and Sept. 1.
(Reporting by David Milliken, editing by Andy Bruce)