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The next round of Brexit trade talks was canceled due to the outbreak of the coronavirus.
Around 200 negotiators should meet in London on Monday for face-to-face discussions.
As the numbers put down by Covid-19 continue to increase worldwide, it was decided to postpone the talks.
It is also unclear whether they can continue using the video link.
In a joint statement, both sides said: "Given the recent developments at Covid-19, negotiators in the UK and the EU today decided not to hold the next week's negotiating round in London as originally planned.
"Both sides are currently looking for alternative ways to continue the discussions, including using video conferencing where possible."
The first round of talks took place two weeks ago in Brussels.
But cabinet minister Michael Gove pointed out that the meeting may not take place on Monday when he appeared before a Commons committee on Wednesday.
He said: "It is a live question. We were looking forward to a joint committee in the UK on the 30th and we were looking forward to the next phase of the negotiations, but we received indications from Belgium today that there may be concrete concerns regarding public health. "
The postponement will likely lead to new demands for an extension of the Brexit transition period, which is expected to end on December 31, as there is no end in sight to the coronavirus crisis.
Downing Street has insisted, however, that Boris Johnson will not make such an application to ensure that Britain no longer complies with all EU regulations by 2021.