An emotional Mrs May announced today she was quitting outside 10 Downing Street and will leave her post on Friday, June 7.
The Tory party will now seek to elect a new leader and it is expected to a a pro-Brexit MP.
Said the Foyle MLA: “Attempts to implement Brexit have now cost the British Government 38 Ministers since the 2016 referendum, including two Prime Ministers.
“It is a doctrine that seeks to sink an axe of simplicity into the delicate layers of political relationships across Ireland. And it has broken old political certainties in Britain.
“It is fundamentally an undeliverable prospect.
“I have disagreed with Theresa May almost every single step of the way over the course of the last three years.
“Triggering Article 50 with no plan to prevent a hard border in Ireland, reneging politically on the agreed terms of the backstop and stubbornly refusing to call a halt to the madness that has consumed Westminster.
“It is undeniable, however, that she has exhausted every avenue to find agreement in the House of Commons.
“The simple fact remains, however, that there is clearly no consensus to be found.
“The European Union has already said very clearly that the Withdrawal Agreement is not up for renegotiation.
“A new Prime Minister should recognise the mistakes made by Theresa May, revoke Article 50 and put an end to this political, diplomatic and economic car crash,” added the SDLP leader.