There has been uncertainty over whether May will still be able to pursue a "hard Brexit" after a humiliating defeat in the general election left her short of a parliamentary majority and requiring the support of other parties.
Besides forging a deal to keep her job and preparing for Brexit talks, May is also grappling with a crisis over the breakdown in power-sharing between the pro-British DUP and the Catholic nationalist Sinn Fein party in Northern Ireland's separate, devolved government.
Now the Tories are seeking an agreement with Northern Ireland's DUP in order to form a government.
It noted how Article 50 of the Lisbon Treaty states divorce talks should take account of a departing member state's future relationship with the bloc.
The negotiators aim to wrap up a deal by the end of 2018 so that it can be ratified by the European and British parliaments before the United Kingdom leaves the bloc in March 2019.
More pressing is the issues of providing effective guarantees to some 5 million people - around 3 million European Union citizens living in Britain plus nearly 2 million Britons in Europe - who want to know what the future holds after Brexit.
Britain has announced that Brexit negotiations will begin on June 19, despite earlier speculation they could be delayed, as Prime Minister Theresa May is still scrambling to prop up her minority government.
"We should be protecting jobs, protecting economic growth and protecting prosperity", Hammond said as he arrived for a meeting of European Union finance ministers in Luxembourg.
"We've set out the broad principles from where we will start the negotiation and we will negotiate in good faith, but it is a negotiation and we recognize there will be an exchange of views and we will take that forward in a spirit of genuine cooperation", Chancellor of the Exchequer Philip Hammond told reporters in Luxembourg on Friday.
A senior Brussels official said the amount, which compares to London's annual net European Union payment of around 10 billion euros, would still be "peanuts" in terms of the overall economy and also that the final bill would be determined less by technical and legal arguments than by hard-headed political horse-trading. "The withdrawal and future are intimately linked".
"Our view is that withdrawal agreement and terms of the future relationship must be agreed alongside each other".
London has said it wants formal political talks between Barnier and Brexit minister David Davis to start next Monday but it since Thursday's election it has not formally committed to the date.
Since her gamble on a snap election failed a week ago, May has come under pressure from some in her own party to change her approach to Brexit talks.