David Cameron’s former strategy director is to advise the data analytics firm credited by the director of Vote Leave with swinging the referendum in favour of Brexit. The news has prompted concern about the revolving door between government insiders and business interests.

Ameet Gill, who was Cameron’s director of strategy from 2015 until last summer, is to advise AggregateIQ, the Canadian firm paid more than £3.5m by groups campaigning for a leave vote during last year’s referendum. It specialises in “micro-targeting” users of social media so that political parties can reach them more effectively.

The new role is revealed in a letter to Gill published by the Advisory Committee on Business Appointments (Acoba), the watchdog responsible for monitoring jobs taken up by former civil servants. It raises the intriguing possibility that Gill could help promote the firm in Conservative circles, giving the party a new campaign weapon come the next general election.

Gill now runs his own consultancy, Hanbury Strategy, focusing on Brexit issues, in partnership with the head of the Vote Leave communications team, Paul Stephenson. Documents leaked last year show that the firm provided polling and “advisory services” to the Macron campaign in France.

In October, Acoba criticised Gill for accepting clients without securing its clearance and expressed its anger in a scathing letter to the civil service chief, John Manzoni. “To fulfil the remit given to it by government, the committee needs to be able to consider an application fully and freely before offering its advice,” the committee secretary, Nicola Richardson, explained in the letter. “It is impossible to do this in a way that will command public confidence if an appointment has already been announced and taken up.”

In its response to his original application, the committee warned Gill that he “should not draw on (disclose or use for the benefit of yourself or the organisation to which this advice refers) any privileged information available to you from your time in Crown service” and said that “for two years from your last day in service, you should not become personally involved in lobbying the UK Government on behalf of AggregateIQ, its subsidiaries or clients”.

It is troubling to see one of Cameron’s key advisers take work with a firm accused of hijacking the Brexit campaign. Caroline Lucas

AggregateIQ, which has a staff of roughly 20 and is based in British Columbia, received more than 10% of the £32m spent by both sides during the EU referendum campaign. Dominic Cummings, the director of Vote Leave, is quoted on the firm’s website as saying: “Without a doubt, the Vote Leave campaign owes a great deal of its success to the work of AggregateIQ. We couldn’t have done it without them.”

The company’s apparent success has turned the spotlight on data analytics. But some MPs are uneasy about the role and influence of such firms, questioning whether foreign companies employed by British political campaign groups are adequately regulated.

The Information Commissioner, Elizabeth Denham, has launched an investigation into the use of targeted advertising by political campaigns and is due to publish her findings this year.

“It is troubling to see one of David Cameron’s key advisers take work with one of the firms accused of hijacking the EU referendum campaign,” said Caroline Lucas, the Green party MP. “There’s plenty of evidence to suggest that AggregateIQ had an undue influence on the result of the campaign, hiding behind non-disclosure agreements and the fact that electoral law doesn’t cover foreign firms.”