FILE PHOTO: European Union's chief Brexit negotiator Michel Barnier delivers a speech during a debate on BREXIT after the vote on british Prime Minister Theresa May's Brexit deal, at the European Parliament in Strasbourg, France, January 16, 2019. REUTERS/Vincent Kessler

LISBON (Reuters) - The European Union is open to the possibility of a “more ambitious” Brexit deal than the one rejected by the British parliament, the EU’s chief negotiator, Michel Barnier, said on Thursday.

The crushing defeat for Prime Minister Theresa May’s deal has forced her to sound out other parties for alternative proposals that they could agree to. It also increased the risk that Britain will quit the EU on March 29 without any deal to cushion the impact.

May had expected, after Brexit, to negotiate a wide-ranging free trade agreement for goods with the EU as part of a fully independent British trade policy.

The main opposition party, Labour, wants Britain to be in a customs union with the EU, which would rule this out, and others want Britain stay even closer to the EU by staying in its single market, along the lines of Norway’s arrangement.

“If they (Britain) tell us they want a more ambitious relationship, we are open,” Barnier told reporters alongside Portuguese Prime Minister Antonio Costa during a visit to Lisbon.

Barnier held out no hope that the agreement reached over the course of two years on the principles that May originally set out could be improved on.

Costa said that since this deal had been rejected, “at this moment the next step does not depend on the EU or Barnier” but on Britain.

Earlier, Barnier told a Portuguese parliamentary committee that contingency measures adopted to cope in the event of a disorderly “no-deal” Brexit would be implemented in a climate of distrust.

“If there is no deal, there will be contingency measures,” he said. “But that will be very difficult and will not be done in a climate of confidence. The best guarantee is reaching an agreement.”