Former prime minister Mr Cameron said Mrs May would have to change her approach to Brexit as a result of the election.
She is set to meet with all 10 DUP members of parliament along with unionist and nationalist leaders.
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.
Instead she finds herself faced with accusations that the deal she is trying to make with the DUP could leave the British government open to bias charges in Northern Ireland politics.
Ultimately, Mrs May's need for an ad hoc partnership with the DUP has weakened, rather then strengthened, her hand at the negotiating table.
Concessions on such issues could seriously damage efforts by the DUP to secure a deal with Sinn Fein to restore Northern Ireland's devolved government, which collapsed in January.
Ms May is now engaged in talks with the Democratic Unionist Party over a so-called "confidence and supply" arrangement that give the Conservatives a majority in the House of Commons and the ability to form a government.
"We are today calling on the next UK Government to commit, particularly in the absence of functioning devolution, to prioritise bringing Northern Ireland's abortion laws in line with global human rights standards".
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"I understand there is a new United Kingdom government and changes in the government in the Republic but there remains no impetus to this process, which doesn't inspire confidence", he said.
Secretary of State James Brokenshire and DUP leader Arlene Foster were both in London for talks on the confidence and supply deal that would enable Theresa May's minority government to function.
The accord commits the UK Government to demonstrate "rigorous impartiality" when dealing with competing political views in the region.
In a statement afterwards, Mrs May said that "good progress" had been made and an agreement was possible if there was "good will on all sides".
They've been of the view that leaving the European Union should lessen some of the stipulations in relation to state aid that were being applied by the Treasury to Northern Ireland, and that might take down the bill that the Treasury would put on the executive if corporation tax was lowered. "We want to govern ourselves".
But the other Stormont parties have warned that any deal between the DUP and Conservatives could make restoring power sharing more hard.
The 1998 Good Friday Agreement - also referred to as the Belfast Agreement - commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.