Britain and the European Union are on the cusp of a Brexit deal which could be clinched in the next 24 to 48 hours, Prime Minister Theresa May's de facto deputy said on Tuesday.

While officials choreograph the biggest divorce deal in EU history, it remains unclear whether May can get a deal through Parliament, where opponents have warned she is betraying Brexit by signing up the United Kingdom to EU subjugation.

"We're not quite there yet," Cabinet Office Minister David Lidington told BBC radio. "We are almost within touching distance now."