Exiled opposition leaders have formed a coalition, and the grouping is now seeking international recognition as a government-in-waiting.
Western powers demanding Syrian leader Mr Assad step down and end the 19-month rebellion have been frustrated by squabbling among his opponents.
"It is a very important milestone," Mr Hague said at a meeting of ministers at the Arab League in Cairo yesterday.
"We want the Syrian opposition to be inclusive ... and to have support inside Syria, and if they have this we will then recognise them as the legitimate representative of the Syrian people."
He said that did not imply Britain would be ready to send weapons to the opposition. The European Union currently has in place an arms embargo on Syria.
But he added: "We are not excluding any option ... the Syrian crisis is getting worse all the time."
Some 2.5 million people have been internally displaced by the country's civil war, the United Nations refugee agency said.
"The winter cold and rain will heap further misery on soaring numbers of Syrian refugees," Mr Hague added.