The former prime minister Gordon Brown has backed calls for a second Brexit referendum and said Britain should leave the door open to rejoining the European Union if it leaves as planned next March.

Speaking in London, Brown said MPs should be prepared to tell the government to renegotiate with Brussels should the Commons be unhappy with a proposed deal, but that at some point the public would demand another say.

“I believe a referendum will happen as people come to the conclusion that since 2016 the situation has changed and at some point they will want to have the final say,” Brown said in a speech at the Institute for Government thinktank.

He called for the setting up of a royal commission to take evidence from leave and remain voters in order to heal the divisions caused by the 2016 Brexit vote.

Brown said that more than two years after the decision to leave, none of the important issues – such as what sort of relationship Britain wanted with the EU and the scope to sign trade deals – had been finalised. Theresa May’s attempt at a quick fix would inevitably be followed by years of talks that would leave the public feeling let down.

“If the next two years of negotiation involve a process as inward looking, divisive and partisan – as dominated and driven by internal Conservative politics as the past two years – we will become an even more divided country, more divided than in the 70s during the three-day week, than in the 80s during the miners’ strike and than in the early 90s because of poll tax.”

Brown’s intervention in the Brexit debate came as Theresa May faced hostility from Conservative remainers and Brexiters over her proposed deal with Brussels.

Brown said there had been none of the careful assessment of the issues that had been undertaken by Harold Macmillan’s government before Britain first applied to join what was then the Common Market in the 1960s, or when he as chancellor was weighing up the pros and cons of joining the euro.

“The failure to agree and the prolonged uncertainty that arises, means ignoring the real long-term challenges – the four major threats for the future – long-term investment plans by companies put at risk; the union put at risk; British global influence in danger of reaching its lowest-ever ebb and Britain’s social cohesion in jeopardy because of our failure to face up to the issues raised in the Brexit vote.”

Brown said it was important to tackle the grievances that had led to 52% voting to leave the EU, but added it was possible to deal with issues such as managing immigration while being an EU member.

The toxic atmosphere was creating “fertile ground for populist politicians whose main claim is not that they offer serious alternatives but whose stock in trade is to articulate people’s anger”, he said.