Engel was the Labour MP for North East Derbyshire between 2005 and 2017 and has been deputy speaker of the House of Commons, as well as an active trade unionist, before her parliamentary career.
After stepping down as an MP, Engel became the commissioner for shale gas, where she led efforts to encourage the best use of Britain’s onshore gas reserves until earlier this year.
Engel said the agency understand how decisions are made in Government. "You don’t change politicians’ minds by meeting them for quiet chats."
She added: "You change their minds by giving them detailed policies they can implement and that can win them votes, and by applying pressure on them by mobilising persuasive voices in high-impact campaigns."
The non-partisan agency operates on a projects-only model and recently worked with Google, Oxford University and the Department for International Trade.
Staff at the agency include Gabriel Milland, former deputy director at the Government Communications Service and head of comms for two government departments.
James Frayne, founding partner of Public First, said: "Natascha combines deep policy interest and campaign expertise, with an encyclopaedic understanding of how Parliament works and how the Labour Party works. She will give our policy and campaign projects a new edge."
In January, PRWeek named Public First as one of its 'UK PR agencies to watch in 2019'.