The audit is being run by LLM co-founder John Mendelsohn, who will report findings in approximately three months.
The agency won the account in a three-way pitch.
The audit will be overseen by the Design Council’s recently appointed government relations manager Dr David Webster, who took up the post in May.
The Design Council is a non-departmental public body that aims to inspire and enable the best use of design in the UK.
Webster said: ‘My role is to develop and conduct a government relations strategy that reflects our mission and values.’
Design Council senior manager of media relations Helen Thompson said the audit was not expected to highlight serious issues for its government relations but would help Webster implement a fresh strategy.