Hill was speaking at a breakfast briefing organised by the agency Champollion, of which he is a director, to assess the political state of affairs the UK finds itself in as the two major parties prepare for their annual conferences.
The EU referendum and resulting Brexit, Labour disunity and the appointment of Theresa May as Prime Minister and leader of the Conservatives were all under the spotlight at the event, held in Westminster on Thursday morning.
In a Q&A following the panel session, in which Hill had told the audience that Labour disunity could add an additional 15 years to its march back to electoral victory, he told PRWeek that the party must fight on the issues on which it is united.
He said: "A very important message to convey is that we may have problems in terms of internal organisation, but what we can do is concentrate on calling the Government to account on issues where we are united... Brexit, grammar schools and health. These are really big frontline policies where we can attack effectively."
She added: "She needs to articulate this by pulling together that sense from her personality, together with some indication in her speech that there is some consistency there and that she is not presenting a series of ad-hoc policies."