* May yet to strike a deal to prop up her minority government
* Pressure mounting for change in Brexit strategy
* PM has to keep pro-European and Eurosceptic factions happy
By William James and Alistair Smout
LONDON, June 14 (Reuters) - Britain entered a sixth day of political limbo on Wednesday with Prime Minister Theresa May yet to seal a deal to prop up her minority government and facing calls to soften her stance on Brexit days before negotiations on leaving the EU begin.
May’s team will resume talks with Northern Ireland’s Democratic Unionist Party (DUP) on a deal to secure their support in parliament after the 60-year-old leader failed to win an outright majority in last week’s election - a vote she called expecting to strengthen her position.
Instead, the shock outcome has left May weakened among her Conservative Party and thrown open her Brexit strategy to criticism from peers, some of whom want to ditch the current plan to leave the European Union single market and customs union.
May said on Tuesday that talks with the DUP had been productive - a view shared by DUP leader Arlene Foster - and that Brexit negotiations would begin as planned next week.
“I think there is a unity of purpose among people in the United Kingdom,” May said following a meeting with French President Emmanuel Macron on Tuesday.
“It’s a unity of purpose, having voted to leave the EU, that their government gets on with that and makes a success of it.”
But pressure was mounting for May to change course on the type of Brexit Britain should pursue.
The Times newspaper said finance minister Philip Hammond would push May not to leave the customs union - an arrangement which guarantees tariff-free trade within the bloc but prohibits members from striking third-party trade deals.
The report cited unnamed sources, and the finance ministry declined to comment.
Nevertheless, it illustrated the challenge May will face in the remaining days before the EU divorce talks begin: finding a position that satisfies both pro-European and eurosceptic factions of her party if she wants to remain in power.
May will also be reliant upon the 10 lawmakers from the eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing.
But a deal with the DUP also risks destabilising Northern Ireland by increasing the influence of pro-British unionists. They have struggled for years with Irish nationalists, who want the British province to join a united Ireland.
Former British Prime Minister John Major said he was concerned May’s plan to govern with the support of the DUP could pitch the province back into turmoil by persuading ‘hard men’ on both sides of the divide to return to violence.
Irish nationalist party Sinn Fein said the prospect of a British agreement with the DUP was causing anxiety and fear.
While the DUP are deeply eurosceptic, they have balked at some of the practical implications of a so-called hard Brexit -- including a potential loss of a “frictionless border” with the Republic of Ireland -- and talks will touch on efforts to minimise the potential damage to Northern Ireland.
Brexit minister David Davis has insisted the approach to the EU divorce has not changed, but May has recognised that a broader consensus needs to be built for Brexit and has made clear she would listen to all wings of the party on the issue.
She will have to manage conflicting demands from within her own party, including a proposal for business groups and lawmakers from all parties to agree a national position for Britain’s most complex negotiations since World War Two.
Former Prime Minister David Cameron said May needed to listen to rival political parties, and that there would be pressure for a softer Brexit.
May faces a difficult balancing act. Divisions over Europe helped sink the premierships of Margaret Thatcher, Major and Cameron, and many of her lawmakers and party membership support a sharp break with the EU.
The performance of the British economy could also influence perceptions of Brexit. Government bond prices suffered heavy losses on Tuesday after consumer price inflation jumped to 2.9 percent in May.
As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.
The veteran conservative predicted that Britain would regret its departure from the bloc at some point in the future.
France’s Macron said the EU’s door was still open for Britain as long as the negotiations were not finished, but that it would be difficult to reverse course. (Reporting by William James and Alistair Smout; Editing by Tom Brown)