Ms Brady was advised that “there should be engagement at a political level before a final decision is taken” on a press statement.

In separate emails, the Executive Office official advised having a “conversation with FMdFM (first minister and deputy first minister) and the finance minister” before finalising a statement.

The official drafted a “holding line” which said the NICS would have internal discussions before making a decision on this year’s Pride parade.

But a senior Department of Finance (DoF) official responded: “For a number of reasons I don’t think we should say that.”

The official added that NICS participation “as an employer” was “different to political attendance”.

A note of a meeting in June said the finance minister – Sinn Féin’s John O’Dowd, whose department has responsibility for civil service matters – was “content for NICS to retain a presence at Pride”.

Traditional Unionist Voice (TUV) criticised the continued involvement of NICS in the parade.

The party’s equality spokesperson Ann McClure, who submitted the FOI, said the NICS was “fully aware of the political sensitivities” but “pressed ahead regardless”.

She questioned whether deputy first minister Emma Little-Pengelly, of the Democratic Unionist Party (DUP), was consulted.