"We have to keep up the pressure for that orderly transition we have called for to visibly take place," Foreign Secretary William Hague told BBC television on Sunday.
He called for "a real, visible and comprehensive change that will bring people together in Egypt."
Pressed on the details of the transition, Hague suggested that it might entail "some mixture of a more broadly based government that includes people from outside the ruling elite of recent years."
But he stressed foreign powers could not impose a detailed plan on Egypt, where protesters on Sunday continued to occupy Cairo's Tahrir Square in the revolt against President Hosni Mubarak's rule.
"We can't lay down or enforce the detail, Egypt is a sovereign nation," he said.
"It is not our role to say the president must go on a particular day or this individual must be included in the Egyptian cabinet," Hague added.
The Brotherhood, a well-organised Islamist movement, has long been banned from Egyptian politics, and the invitation from Mubarak's camp is a historic turning point.