[4] Robbins was appointed as Principal Private Secretary to the Prime Minister at 10 Downing Street in 2006, replacing Ivan Rogers for the last part of Tony Blair's administration and the start of Gordon Brown's.

In this role, Robbins negotiated with The Guardian on how to curtail its reporting of material leaked by Edward Snowden relating to the operations of the CIA and GCHQ.

[11][22] Robbins's role in negotiating a deal for the UK's withdrawal from the European Union led to some Conservative MPs blaming him for an anti-Brexit "establishment plot", criticising him as "secretive" and comparing him to Grigori Rasputin.

[23][24] Acting Cabinet Secretary Mark Sedwill sent a letter to The Times defending Robbins, highlighting that civil servants implement the decisions of elected governments.

[25] Sedwill pointed to the example of HMRC Permanent Secretary Jon Thompson receiving death threats after giving evidence to MPs about the costs of a potential post-Brexit customs plan.

[26] Responding to Sedwill's letter, Andrew Adonis said that civil servants should "start getting used to criticism", as they had the option to work on other policies.

[27] A group of former military and intelligence officials associated with pro-Brexit pressure group Veterans for Britain including the former head of the Secret Intelligence Service Richard Dearlove said Robbins had "serious questions of improper conduct to answer" over defence and security co-operation between the UK and the EU after Brexit.

[27] Former Department for Work and Pensions Permanent Secretary Leigh Lewis backed up Sedwill's letter, noting the "occupational hazard for senior civil servants to be held responsible for the political decisions of ministers", of which he considered the attacks on Robbins to be a blatant example in a particularly toxic environment.

[29] He took up the Heywood Fellowship at the Blavatnik School of Government in September 2019, after which he joined Goldman Sachs as a managing director in the bank's investment banking division; joining former European Commission President Jose Manuel Barroso, who was the non-executive chairman of Goldman Sachs International at the time.