It comes as a separate poll showed more than half of business leaders had seen a negative impact on their companies from the referendum.
Sterling has fallen by 17% against the dollar since the vote to leave the EU in June and the weakness means imported goods and raw materials are more expensive.
A survey by the British Chambers of Commerce (BCC) showed more than two thirds of firms expected the fall in the pound to push up their costs.
The poll of nearly 1,500 businesses carried out in December found 54% expected to have to pass this on by increasing the prices of products and services over the next 12 months.
Exporters were seeing some benefit from the lower pound - as their foreign currency sales translate into higher sterling value - but almost as many said the weakness was damaging them.
BCC director-general Adam Marshall said: "The depreciation of sterling in recent months has been the main tangible impact that firms have had to grapple with since the EU referendum vote.
"Rising costs are squeezing margins, and forcing many firms to increase the prices of their goods and services."
Inflation in December rose to 1.6%, its highest level in more than two years, and is expected to increase further as the effect of the fall in the pound feeds through.
Meanwhile, a poll of more than 100 leaders of the UK's top 500 companies by Ipsos MORI showed 58% felt that the referendum had already had a negative effect on business.
The figures showed 31% felt Brexit had not made any difference while 11% said it had made a positive impact.
They showed 66% felt the result of the referendum would be negative for their company.
Ipsos MORI chief executive Ben Page said: "Unfortunately, it looks like business in this country is already feeling the pain of economic upheaval of leaving the EU."
Looking further ahead, 32% of firms felt Brexit would have a positive impact in five years' time compared to 45% who believed the impact over this period will be negative.
Elsewhere, a submission by the CBI ahead of next month's Budget pointed to inflationary pressures facing businesses including the increase in the national living wage and the apprenticeship levy.
It is calling for a shake up of business rates, urging the Government to support companies at a time of rising uncertainty.
Economic growth has responded more robustly than expected since the referendum, though many experts still expect a growth slowdown this year.
However, the Bank of England last week upgraded its forecast for 2017.
There was further positivity on Monday from the manufacturing sector, with a poll by accountants BDO showing confidence at a 20-month high.