LONDON, June 14- A deal between Northern Ireland's Democratic Unionist Party and British Prime Minister Theresa May's Conservatives could be delayed until next week after a fire in an apartment block in central London killed several people on Wednesday, the BBC reported. Media had reported a deal, which would see the DUP support May's minority government, was on course to be announced on Wednesday. The BBC said that would now not happen, a delay which could possibly postpone Brexit talks due to begin next week. 'Deal between DUP and government could be delayed until next week because of aftermath of #grenfelltower and diary commitments of both leaders,' BBC political reporter Norman Smith said on Twitter. 'Sources say delay over government deal with DUP not because talks are 'stuttering' - 95 percent agreed between both sides.'