The report, Added values: The importance of ethical leadership, found that 9% of managers have been asked to break the law at work, while one in 10 have left their jobs as a result of being asked to do something that made them feel uncomfortable.
In the survey of more than 1,000 managers across the public and private sectors, 93%, said their organisation had a values statement but more than two-fifths (43%) had been pressured to behave in direct violation of it, with 12% of managers saying that the correlation between employee behaviour and company values was not close "at all" in their workplace.
It also revealed 27% of respondents were concerned their career would suffer if they were to report an ethical breach, with whistleblowing fears higher among more junior managers than directors (9%).
Charles Elvin, chief executive of the ILM, said: "As well as damaging a company's reputation, we see that ethical failings can have a negative impact on employee happiness, loyalty and trust in their organisation.
"Not all ethical decisions will be black and white, but an explicit and consistent set of values which are embedded within the organisation and reflected across all of its actions - from strategic decisions down to day-to-day activities - will lay the foundations for ethical behaviour."
Elvin added: "Leaders and managers, including those at more junior levels, have a crucial role to play in communicating their organisation's values and should be given the support they need to enable cultural change."
Stephen Howard, chief executive of BITC, said: "Cultural change is not something that can be instilled in organisations overnight, but this research indicates where some of the key pressure points lie.
"The importance of junior and middle managers in setting an organisation's ethical tone cannot be overestimated - they often feel squeezed and are skeptical about how well corporate values map to their own, are relevant to their work or are demonstrated by their colleagues."
Howard continued: "Responsible leaders must make sure the managers throughout their organisation are involved in the creation of values and understand how those values apply to their day to day work.
"Otherwise they cannot be sure the values as written are the ones that are lived, exposing their organisation to potential ethical breaches and reputational risk."