A small but noisy clutch of anti-Brexit protesters greeted Boris Johnson as he arrived.

Britain has still not proposed any workable alternatives to the Northern Ireland "backstop" provisions of its Brexit withdrawal agreement, the EU said Monday after talks between bloc chief Jean-Claude Juncker and UK Prime Minister Boris Johnson.

The first face-to-face encounter between Boris Johnson and European Commission president Juncker failed to yield any major breakthrough, although Downing Street insisted it had been a "constructive meeting".

Boris Johnson says Britain will not agree to a divorce deal that includes the backstop, a provision which temporarily keeps the UK in the EU customs union to keep the Irish border open, and will not delay Brexit beyond October 31, even if it means leaving with no deal.

Juncker's office said he used the lunch meeting in Luxembourg to reiterate the EU view that it is Britain's responsiblity to come up with a workable alternative to he backstop, which was agreed by Boris Johnson's predecessor Theresa May but rejected by MPs.

"President Juncker recalled that it is the UK's responsibility to come forward with legally operational solutions that are compatible with the Withdrawal Agreement," a statement from Juncker's office said.

"President Juncker underlined the Commission's continued willingness and openness to examine whether such proposals meet the objectives of the backstop. Such proposals have not yet been made."

Alongside the main meeting, EU chief Brexit negotiator Michel Barnier also held talks with British Brexit Minister Stephen Barclay.

A small but noisy clutch of anti-Brexit protesters greeted Boris Johnson as he arrived and left the talks, singing the "Ode to Joy" EU anthem, waving flags and chanting slogans.

With just six weeks to go before Brexit day, the two sides have agreed to step up the pace of talks, Downing Street said, with negotiators to start meeting "soon" on a daily basis rather than twice a week as at present.

"It was agreed that talks should also take place at a political level between Michel Barnier and the Brexit Secretary, and conversations would also continue between President Juncker and the prime minister," a spokesperson said.