(CNN) The Brexit strategy of British Prime Minister Theresa May was dealt a serious blow on Monday with the unexpected resignation of the cabinet minister directly responsible for managing the process of leaving the European Union.

David Davis declared he could not support the deal drawn up by May to unite her divided cabinet, saying it involved too close a relationship with the EU and gave only an illusion of control being returned to the UK after Brexit.

"It seems to me we're giving too much away, too easily, and that's a dangerous strategy at this time," Davis said in a BBC radio interview Monday morning.

Brexit Ministe David Davis leaves 10 Downing Street in central London after attending the weekly cabinet meeting on July 3.

Dominic Raab, a junior minister for housing policy, will replace Davis as Brexit Secretary, Downing Street announced. Raab is an ardent supporter of Brexit.

All eyes are now on the pro-Brexit Foreign Secretary Boris Johnson, who is due to make a statement late Monday afternoon local time. If Johnson also resigns, May's ability to remain as Prime Minister would be seriously weakened.