Calls for a public inquiry into Brexit are mounting among diplomats, business figures, peers and MPs, amid claims that the civil service is already planning for a future investigation into how it has been handled.

The decision to call the referendum, the red lines drawn up by Theresa May and Britain’s negotiating strategy are all issues that senior figures would like to be examined.

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Bob Kerslake, the former head of the civil service, said an inquiry was needed into “the biggest humiliation since Suez, certainly since the IMF crisis [in 1976]”. The cross-party peer said he believed the civil service “is both expecting and preparing for this”.

“We do need to understand how on earth we ended up where we have and it probably needs to go back to the decisions around holding a referendum and the way the question was framed,” he said. “It would need to be a public inquiry, probably judge-led.”

Peter Ricketts, the former national security adviser and former head civil servant in the Foreign Office, cited the Chilcot inquiry into the Iraq war. “Chilcot took a long time, but it was cathartic,” he said. “The report was widely seen to have done the job and I think you can say the British system is better for it. I think the handling of Brexit has been such a failure of the process of government, with such wide ramifications, that there needs to be a searching public inquiry.

“What advice was given to ministers? Was it taken? Did the processes of collective cabinet decision-taking work? Were the right skills available, for example on no-deal planning and all the costs involved? They are all legitimate questions for an inquiry. It should have the powers of a judicial inquiry.”

One senior Tory peer said: “We want our Chilcot.”

Sir Mike Rake, the former chair of BT, said: “When the dust has settled, there really should be some kind of public inquiry, looking at both the issues around holding a referendum and the context of what has happened in terms of pursuing Brexit.”

Many figures are already pointing to May’s early decision to set out strict red lines that seriously limited Britain’s ability to negotiate. John Kerr, Britain’s former EU ambassador who drafted the article 50 process of leaving the bloc, said: “Those red lines laid down in 2016 emerged with no consultation with the country, the devolved assemblies, parliament or with the cabinet. Then there was the decision to trigger article, 50 still with no agreement in cabinet of where we wanted to end up.”

Sir Jonathan Faull, a former senior EU official, said: “It would be surprising if the events relating to UK withdrawal from the EU were not the subject of one or more inquiries. An important initial question will be when to start. The 2015 election? The 2016 referendum? The article 50 notification? The scope ranges from Whitehall and Westminster to Belfast, Brussels and beyond.”

There is also support in the Commons. Tom Watson, Labour’s deputy leader, said: “The government’s handling of Brexit has been a shambles from start to finish. It was a dereliction of duty to allow the country to get to this point, days before Brexit, in danger of crashing out with no deal or trying to force parliament to accept a deal it’s already rejected twice. We will certainly need a detailed postmortem of how this all came to pass.”