At least 12 people died and dozens more were injured when a fire ripped through a tower block.
After more than an hour of talks between Mrs May and DUP leader Arlene Foster on Tuesday, Mrs May said the discussion had been productive.
"The danger is that however much the government tries, they will not be seen to be impartial if they are locked into a parliamentary deal in Westminster with one of the Northern Ireland parties", Major said.
If the Government cannot even secure a deal with the DUP, how on Earth can they get a deal with the EU?
That border will become an external European Union border after Brexit and there have been growing fears that any border controls would have a serious economic impact on both Northern Ireland and the Republic.
Before the election, May proposed a clean break from the European Union, involving withdrawal from the European Union single market, limits on immigration and a bespoke customs deal with the EU.
Her failure to win a majority has put May under pressure over her Brexit plans from inside and outside her party and has prompted complaints about her choice of partner due to the DUP's stance on social issues such as gay marriage. "I can't negotiate with myself", he told The Financial Times. "The reality is that where we stand follows logically from leaving, so, if we're leaving, what we need to do is do it smoothly and successfully and gain economic benefit".
Demanding a swift start to Brexit negotiations under Article 50 of the European Union treaties, the former Belgian prime minister compared Britain's position to the heroine of Lewis Carroll's Alice In Wonderland, who found herself in a room with many doors and no idea what lay behind them. But like Alice In Wonderland, not all doors are the same.
"It will be a brand new door, with a new Europe, a Europe without rebates, without complexity, with real power and with unity".
A senior Conservative source said: 'We are making a lot of progress. "We will be asking the prime minister to be open with politicians and also with the public", SDLP leader Colum Eastwood said in a statement. Data on Wednesday showed average weekly pay in the three months to April fell by 0.4 percent on the year in inflation-adjusted terms - the biggest fall since the three months to September 2014. To do so, she will be heavily reliant on the 10 lawmakers from the eurosceptic DUP, who can help her edge past the 326 votes needed in Parliament to avoid the collapse of the government.
"The UK government is offering whatever support we can, working alongside the Irish government, as appropriate, honouring our respective commitments in the Belfast Agreement to serve the interests of the whole community in Northern Ireland", he said.
Both sides had hoped that a deal would be announced on Wednesday.
Michelle O'Neill, Sinn Fein's leader in Northern Ireland, said any deal between the Conservatives and the DUP "cannot be allowed to undermine" the province's peace accords.
But the Government will press ahead with the first round of Brexit talks two days before the official opening of Parliament.