The European Union hopes for a quick British parliament vote on Britain's withdrawal from the bloc and clarity its plans following Prime Minister Boris Johnson's triumph in elections, the head of the European Council said.

Charles Michel congratulated Mr Johnson and also said the EU was ready to negotiate a free-trade agreement with Britain but called on the British government to work in good faith.

"We expect, as soon as possible, a the vote by the British parliament ... It's important to have clarity, as soon as possible," Mr Michel told reporters as he arrived for a second day of an EU leaders summit.

"We are ready," he said of trade talks.

EU leaders are expected to put in motion preparations for the negotiations on the future relationship between Britain and the EU, which will begin soon after the UK leaves.

Arriving at the summit yesterday, Taoiseach Leo Varadkar said he hoped for a decisive result.

Mr Johnson's landslide victory delivers a brutal clarity to the issue that has been strangling the British body politic for three-and-a-half years. 

The result extinguishes any of the diminishing hope in European capitals that Brexit might somehow be reversed, and EU leaders are likely to welcome the end of months of parliamentary paralysis.

The margin of victory means Mr Johnson will not be held hostage by hard Brexiteers in his party, meaning he could potentially go for a closer trading relationship with the EU than he has signalled so far.

However, leaders are expected to resist any attempt by the UK to set the agenda and schedule of the trade negotiations. 

Mr Johnson has emphasised speed, but European capitals will focus on the quality of the future relationship.

The trade negotiations will be bruising, but Mr Johnson at least has a free hand, once he has decided what kind of relationship Britain actually wants with Europe.

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European Commissioner for internal markets Thierry Breton said Britain's post-Brexit phase will begin on 1 February as there is now little doubt the UK parliament will accept Mr Johnson's exit deal.

"Boris Johnson will have a large majority... It seems logical to consider that (Johnson's Brexit deal with the EU) will be accepted by parliament, and therefore withdrawal on January 31st, which means we will be in the post-Brexit phase from February 1st," Mr Breton, a Frenchman, said on French radio RTL.

"The Brexit negotiations are over now. We are now entering a phase of trade talks between Britain and the EU."

Additional Reporting Reuters