Meanwhile, about the same proportion said currency was having a negative impact on their profitability.
The BCC said rising import costs were "squeezing" SMEs' margins.
Sterling has fallen by around 16% against the dollar since Britain voted to leave the EU last June.
Dr Adam Marshall, director general of the BCC, said inflation would be an "important concern for businesses over the coming year".
"The depreciation of sterling... has been the main tangible impact that firms have had to grapple with since the EU referendum vote," he said.
"For firms that import, it's now more expensive, and companies may find themselves locked into contracts with suppliers and unable to be responsive to currency fluctuations."
The BCC - which canvassed around 1,500 small and medium-size businesses - found that more than two thirds expected input costs to increase this year due to the weak pound.
And while one in four exporters said they had seen a beneficial impact from currency movements, almost the same number saw a negative impact.
Last week, the Bank of England forecasted inflation would run at 2% this year - slightly higher than its previous forecast of 1.8% made in November.
However, it also said it expected the economy to grow at 2%, up from a previous forecast of 1.4%.
The bank said domestic demand had been stronger than expected following the referendum and there were "relatively few" signs of a slowdown in consumer spending.
However, it still sees the economy slowing in 2018, when it expects growth of just 1.6%.