Clearly, the group of 12 Scottish Conservatives will play a major role here, given that leader Ruth Davidson has called for a more open Brexit.
"I want to reiterate at the outset of these talks that the United Kingdom will remain a committed partner and ally of our friends across the continent".
International Trade Minister Liam Fox will travel to Washington on Monday to explore new trade ties - although no formal negotiations are possible until Britain has actually left the bloc.
May, under pressure after losing her ruling Conservatives' majority in a botched snap election and over her response to a devastating fire that killed at least 58 in a London apartment block, says she wants a clean break with the European Union - a strategy some in her party have challenged as risking economic growth.
Marshall said businesses were realistic about the complex nature of Brexit talks, but that they were keen to see some "quick wins". The proper - only - response to this attack is for the rest of us to show more decency, restraint and solidarity with each other, not less.
Soros argued if May is to continue in power then she must change her political approach.
"It's important to remember that negotiations on some of the most crucial business issues, such as the nature of the future UK-EU trading relationship, won't begin straight away".
European stocks rose today, partly on optimism about the talks actually getting underway after months of sniping and uncertainty, analysts said.
Is Britain also looking for a free trade deal?
"We're leaving the EU and because we are leaving the EU, we will be leaving the single market and by the way, we will be leaving the customs union".
Barnier, meanwhile, made clear that a price would have to be paid for the unprecedented split.
Other issues on the agenda, at least in the near term, include establishing residential rights of more than 3 million European Union citizens now living in the United Kingdom - and the 1 million British expats living in European Union member states - once the formal exit is complete.
The government's current weakness has fuelled criticism of its approach to Brexit and given rise to notions that the government might pursue a softer tone.
"We each have to assume our responsibility and the consequences of our decisions", he said at the conclusion of Monday's press conference.
"There is a growing consensus across the parties, in business and amongst the public, that an extreme "hard" Brexit of the kind put forward by Theresa May at Lancaster House is no longer politically viable and would be economically disastrous".
The storm clouds began to gather in the immediate aftermath of the referendum, when investors quickly sent the pound to its lowest level in decades over fears that Britain would lose preferential access to Europe's vast markets.
No deal would be "very, very bad" for Britain, Hammond said, but worse would be a deal "deliberately structured to punish us, to suck the lifeblood out of our economy".
- Ivana Kottasova contributed reporting.