In an article in the Mail on Sunday newspaper, Boris Johnson wrote that May's Brexit plan wrapped "a suicide vest around the British constitution" and the EU holds the detonator.

"There has not been a (leadership) challenge," David Lidington, minister for the Cabinet Office, said during an interview with CNBC, following new comments from former Foreign Affairs Minister Boris Johnson criticizing Theresa May.

Despite renewed criticism of the U.K. prime minister's approach to Brexit negotiations, the majority of the Conservative Party still supports Theresa May and her efforts to take the country out of the European Union (EU), a senior member of the U.K. government told CNBC on Sunday.

Johnson, a vocal Brexit supporter, resigned from the U.K. government in August because he didn't agree with the prime minister's plan for Brexit. Some political analysts and U.K. media have interpreted his resignation as a way to challenge Theresa May and take over her role, although it's unclear how much support Johnson has within the party.

"The huge majority of conservative MPs and conservative party members in the country want to see Theresa May continuing to lead us in getting the right deal," Lidington told CNBC's Steve Sedgwick on the sidelines of The European House Ambrosetti Forum.

Speaking on the Brexit process, Lidington added that the key to closing the negotiations is the Irish border issue.

"Both we (the U.K. government) and the commission reckon we are about 85 percent to agreeing the formal legal text. What's left is mostly the Irish backstop and intensive discussions are ongoing about that now," he said.

European leaders are due to meet in Salzburg, Austria, on September 20th, where Brexit will feature the discussions.

Lidington is hopeful that such meeting will pave the way for a deal between the U.K. and the EU "either (in) October or November this year."