The study, by FH and Jigsaw Research, surveyed communications directors from leading brands and members of the public.
It found that 64% of the public did not believe that companies' marketing and comms were backed up by the way they behaved and interacted with customers.
Additionally, just 15 per cent of the public would trust a company again that had offered an apology or explanation from a senior executive following a crisis.
However, 60 per cent would believe an apology if there was evidence that their behaviour had changed for the better through improved customer service and positive business behaviour.
A total of 52% of respondents said they did not believe business or brand "stories" if they were only told through advertising and communications.
The study found these stories were more believable if they extended to customer service and the overall behaviour of that business, but 20 per cent said they did not believe brand stories at all.
Fishburn Hedges Group chief executive Simon Matthews said: "Audiences can see right through business messages that don’t correlate to behaviour. Corporate communications has an opportunity to help unify different organisational voices and bridge the gap between them to be a force for cultural good within the business. Whether we are talking about storytelling or corporate narrative, the reality now is that they aren’t being driven right through a business."
FH and Jigsaw Research undertook qualitative interviews with 20 communications directors from leading brands, including Unilever, Telefonica and The Body Shop, between May and August 2013, and commissioned OnePoll to survey 1,000 UK adults in August 2013.