Verhofstadt told BBC Radio 4’s Today programme: “All British citizens today have also EU citizenship. That means a number of things: the possibility to participate in the European elections, the freedom of travel without problem inside the union ...

“We need to have an arrangement in which this … can continue for those citizens who on an individual basis are requesting it.”

But the former Belgian prime minister said the European parliament was committed to ensuring that countries outside the EU did not have a better deal than member states.

He also warned that the parliament would have the power to veto any deal brokered between the UK and European commission.

Verhofstadt claimed to have received more than 1,000 letters from British citizens who do not want to lose their relationship with “European civilisation” and criticised the remain campaign for speaking “only about economics” rather than voters’ emotional connection to the continent. Some Britons felt they were “losing a part of their identity” by having their EU citizenship taken away, he said.

He described Brexit as a “tragedy, disaster, catastrophe” for the EU and said the rights of UK citizens living in the EU and EU citizens living in Britain would be his first priority for negotiations after article 50 is triggered, beginning the formal process of Britain leaving the bloc.

EU and UK citizens “cannot be the victim of the political games we have seen”, Verhofstadt said. Reaching a deal on their futures would be the first chapter of a withdrawal agreement that needs to be finalised by November or December at the latest, he added.

The agreement will also include a deal on the size of the divorce bill and transition arrangements, he said. The remainder of the two-year leaving period will be spent starting to define the nature of Britain’s future partnership with the EU.

Verhofstadt ruled out a return to a “hard border” between Northern Ireland and the Irish Republic, warning that this could threaten the peace process. “What cannot happen is that we destroy all the efforts that have been undertaken [in] the last 20-30 years to have peace there, so no hard border, we cannot return to the hard border,” he said.

The Brexit representative had previously said the EU needed to be “open and generous” to individual British citizens and that politicians were considering how to enable them to maintain their ties to the continent.

He told an audience at Chatham House in January: “We are scrutinising, thinking, debating how we could achieve that. That individual UK citizens would think their links with Europe are not broken.”

In Brussels, the idea of EU citizenship rights for Britons has already been dismissed as a non-starter, with EU insiders pointing to vast political, legal and technical hurdles.

The EU’s 27 remaining member states, which are in charge of Brexit negotiations, would have to rewrite treaties, which governments have repeatedly ruled out in recent years. Several senior EU experts have previously told the Guardian such a plan has no chance of success. “This proposal is absolutely not serious,” one former ambassador said, describing the idea as “very vague and for the distant future”.

EU diplomats also stress that Verhofstadt has no power to put the idea on the agenda of Brexit talks. The Liberal MEP is the parliament’s Brexit representative, but will not have a place at the negotiating table, although the parliament will be informed and consulted.

The former Belgian prime minister hopes to use the parliament’s right to veto the deal – a blunt, but potentially deadly instrument – to set the agenda. But he may face difficulty in winning support from the parliament to hand out meaningful EU citizenship benefits to Britons. MEPs from other political groups believe he would struggle to convince the two biggest groups, the centre-right bloc and the Socialists, to back his idea.

Verhofstadt, who leads the Liberals, the fourth-largest group, does not have unqualified support among MEPs. Privately, some senior MEPs from rival groups have dismissed his claim that the parliament would veto a deal it does not like. A member of one of the largest groups told the Guardian that MEPs would fall into line with their governments once a deal has been reached between EU leaders.

Formal negotiations cannot begin until May triggers article 50, which she has promised to do by the end of March, but the Conservative MEP Vicky Ford told the Today programme the UK and EU were nearing agreement on a potential Brexit divorce bill and the rights of Britons living in other EU countries.

“Both sides are very close on the money,” Ford said. “The EU are saying they will only ask us to contribute what we’ve committed to and the prime minister is saying we don’t walk away from commitments. If that principle is agreed, then we can move on.”

On Thursday, Johnson, the foreign secretary, called on May to emulate Margaret Thatcher and resist EU demands for money, but the Irish taoiseach, Enda Kenny, was among the EU leaders supporting a fee.