After nearly a year of waffling, Britain on Monday finally opens negotiations with its European Union counterparts about leaving the bloc, with the final outcome, due in 2019, as important as it now seems unpredictable.
Mr Hammond appeared to kick the government's 100,000 net migration target into the long grass, saying the focus after Brexit would be to "home-grow the skills we need" before seeking to significantly cut the number of workers entering the UK.
Barnier has said a divorce deal should be ready by October next year to give time for parliamentary approval. The price of such a deal remains unclear. This is however easier said than done, as is the ability to pursue a softer approach in the negotiations. With or without a deal, Britain will be out of the European Union on March 30, 2019. The party has refused to give a time frame for reaching a deal, though May is due in Brussels for an European Union summit on June 22-23 when she will want to show she has a solid grip on power. The prime minister is still trying to secure the support of a fringe party whose votes she needs to form a government.
The sensitive issue has been thrown into further doubt by May's efforts to seek a deal with Northern Ireland's ultra-conservative Democratic Unionist Party to stay in power after the British election.
After facing criticism for not meeting survivors on Thursday, May visited a hospital on Friday to speak to some of the people who escaped the fire.
Britain begins its Brexit negotiations this week in a much weaker position than it was just a month or so ago, though it was weaker than it seemed to imagine.
In the long-term I get the impression that this election result, and what may follow over the course of the next two years and beyond, is now more likely to ensure a far better outcome for the United Kingdom economy than we appeared to be heading for pre-election.
Three key issues will dominate the first phase of the talks.
Asked if that meant no transitional arrangements, she replied: "Well, I'm extremely optimistic that we will find there is a lot we can agree on".
"In my experience recently, businesses that look over the garden fence have gone: "Hmm, (the) grass is not quite as dark and unforgiving as you might expect", Andrew told the BBC.
While the European Union negotiating team led by Barnier has been ready for months, British efforts on Brexit stalled even after it triggered the two-year process on March 29.
But the business community and many lawmakers want to retain closer ties with Europe, and they are heaping pressure on the prime minister to change her approach.
"We should be protecting jobs, protecting economic growth and protecting prosperity", he said in Luxembourg last week.
On her part, Britain's Prime Minister said that she was keen to stick to her planned timetable and would start the Brexit talks in Brussels.
One diplomat said Ms May tried to "hijack" the summit by drawing other leaders into Brexit talks, though European Union officials played down suggestions of any agenda row with London.
Theresa May can ill-afford to alienate this group, or indeed any other within her party.style="text-align: center;"