With Prime Minister Theresa May still working to shore up a deal with a small Northern Irish party to prop up her Conservative government after she lost her parliamentary majority in the June 8 election, Hammond's comments could be a sign that London is easing its approach to Brexit.
May has clung on to power since the election but has so far failed to strike an agreement with Northern Ireland's ultra-conservative Democratic Unionist Party that would allow her to govern.
"We should be protecting jobs, protecting economic growth and protecting prosperity", he said in Luxembourg last week.
British finance minister Philip Hammond said Britain should adopt a pragmatic approach to Brexit negotiations which begin on Monday, striking a different tone to Prime Minister Theresa May who has threatened to leave the European Union without a deal if necessary.
A week after May lost her majority in an election she had called in the hope of strengthening her hand in the talks, some fellow Conservatives want her to focus more on limiting the damage to business and less on cutting immigration and other ties to the European Union when Britain leaves the bloc in March 2019.
An EU official close to the matter said the "softer Brexit" talk could be "productive" and help progress in the first months, where the British attitude to discussing the financial settlement "will be the first serious test of the negotiations".
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"It is good that the British government thinks about the rights of European Union citizens in Great Britain", Verhofstadt said.
Other members of May's Conservatives have called for a more inclusive approach on Brexit strategy that would include the voices of opposition parties as well as the views of Scotland and Northern Ireland, which both voted to stay in the EU.
Mr Hammond said the United Kingdom "should prioritise protecting jobs, protecting economic growth and protecting prosperity".
The Chancellor had been due to use a high-profile speech in the City of London on Thursday night to send out a message the Government would protect business from shocks during the Brexit process.
"We will build the broadest possible consensus for our Brexit plans and that means giving parliament the maximum amount of time to scrutinise these bills by holding a two-year session of parliament", the government said in a statement.
On Monday, the European Commission insisted it was "fully prepared and ready for the negotiations to start" the process.