In Brussels, the belief is that if Prime Minister Theresa May wins a large majority as expected on June 8, she will no longer have to worry so much about upsetting hardliners in her Conservative Party.
That would give her space to consider options that are anathema to core Brexiteers, such as a transitional deal until 2022 in which free movement and the jurisdiction of the European Court of Justice could continue.
European Parliament President Antonio Tajani said as much when he visited May in London on Thursday, adding that a new government before talks start later in June is "good not only for the UK but for us."
The current mood is more promising than when May formally triggered the two-year Brexit process last month, a step that saw both sides taking tough positions on the talks ahead.
London and Brussels have been at odds on whether talks on the divorce arrangements, including costs, should take place at the same time as negotiations for a trade deal between post-Brexit Britain and the EU.
He said May would have the "political capital" to take her own decisions if she increases her centre-right party's current slim majority.
The Conservatives won that in 2015 under David Cameron, who resigned after last June's shock Brexit referendum result. May is not only keen to win her own mandate but also to be less at the mercy of her party's anti-EU right-wing when it comes to parliamentary votes.
Since her election announcement May has adopted a new and softer mantra on a possible Brexit deal, said Giles Merritt of Friends of Europe, another think tank.
Whereas earlier this year May said Britain was ready to walk away and that no deal was better than a bad deal, she is now talking in terms of the "the best deal possible".
"Instead (she will) be open to the sort of arrangements with the EU that hardliners in her Conservative Party have been condemning as a 'soft Brexit'," Merritt said in a commentary.
If so the "positive scenario is that she wants that (a majority) so she's not vulnerable to attacks from the eurosceptic right," Tilford told AFP.
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