British Prime Minister Theresa May was forced to relinquish her two closest aides on Saturday as she struggled to reassert her authority following a crushing electoral setback.
The role of Mr Timothy and Ms Hill as Mrs May's joint chiefs of staff had been severely criticised by disgruntled Tories in the wake of the election result.
Numerous party members are also uncomfortable with the kind of deal that will have to be struck with the DUP, a socially conservative party that takes an opposing stance on issues such as abortion and same sex marriages.
"In particular, I regret the decision not to include in the manifesto a ceiling as well as a floor in our proposal to help meet the increasing cost of social care".
'One of them is country, one of the others is LGBTI rights and I asked for a categoric assurance that if any deal was done with the DUP there would be absolutely no rescinding of LGBTI rights in the rest of the United Kingdom and that we would try to use any influence that we had to advance LGBTI rights in Northern Ireland, ' she said.
But he also set out his concerns about the way the campaign was managed, in comments viewed as a sideswipe at election guru Sir Lynton Crosby.
Ruth Davidson, the Conservative leader in Scotland, said she had asked May for assurances that there would be no attack on gay rights after a deal with the DUP.
May was interior minister for six years before taking over from David Cameron in the political chaos that following last June´s Brexit referendum.
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Writing in The Times she said: "Mrs May condoned their behaviour and turned a blind eye or didn't understand how destructive they both were".
The prime minister has sent a team of officials, led by her chief whip, Gavin Williamson, to Belfast to negotiate the details of an alliance with the DUP.
May remains in 10 Downing Street with a much diminished power base after her Conservative party fell short of an overall majority in the House of Commons, the lower house of the UK Parliament, as the general election results threw up a hung Parliament yesterday.
Numerous key cabinet posts have already been declared as unchanged from the previous government, including Philip Hammond as Chancellor of the Exchequer, Amber Rudd as home secretary, Boris Johnson as foreign secretary, David Davis as Brexit secretary and Michael Fallon as the in-charge of the ministry of defence.
The Queen's Speech setting out the Government's programme is due on June 19, with a highly significant vote on its content expected after a few days' debate.
The DUP has a consistently anti-abortion stance, with its leader Arlene Foster saying: "I would not want abortion to be as freely available here as it is in England".
"From hubris to humiliation", said the left-leaning Guardian.
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