Brexit Secretary David Davis will lead the UK team of negotiators into their fourth round of talks with EU officials in Brussels on Monday.
It will be the first opportunity for the European delegation to respond to Theresa May’s speech in Florence.
Mrs May aimed to restore momentum to a process that was stalling.
Key figures such as EU chief negotiator Michel Barnier described her tone as constructive, which should improve the atmosphere of the talks.
But EU negotiators will be expecting more detail on, for example, what payments the UK is prepared to make as it departs.
Next month, EU leaders are due to decide on so-called separation issues – including the rights of citizens, the Irish border and the “divorce bill” or financial settlement – to allow talks to move on to the future of the bilateral trade relationship, as the UK would like.
For the moment, the odds seem to be against that test being passed at the first opportunity, said BBC Europe correspondent Kevin Connolly.
Budget black hole
In her speech on Friday, Mrs May offered to continue paying into the EU for a two-year transition after the UK leaves in 2019 to ensure the bloc is not left with a budget black hole.
The prime minister sought to reassure member states that they would not lose out financially during the current EU budget period, which runs to 2020.
She also confirmed there would be no restrictions on EU citizens coming to the UK during the transition period, but after Brexit they would be registered as they arrived.
Mr Davis has insisted that Mrs May’s speech was not influenced by a 4,000-word article by Foreign Secretary Boris Johnson, in the run-up to the event, setting out his own vision for Brexit.
The speech “had been coming for a long time”, he said.
Meanwhile, the UK and Scottish governments are due to hold a fresh round of talks on Brexit in London.
Scotland’s Deputy First Minister John Swinney and Brexit minister Mike Russell will meet First Secretary of State Damian Green to discuss concerns about the EU Withdrawal Bill.
And Mrs May holds talks in Downing Street with Irish premier Leo Varadkar, in her first meeting with an EU leader since the Florence speech.