British Prime Minister David Cameron pledged Friday morning that Scotland will have more devolved powers over its affairs, and England, Wales and Northern Ireland must "have a bigger say" over theirs as well.

"It is absolutely right that a new and fair settlement for Scotland should be accompanied by a new and fair settlement that applies to all parts of the United Kingdom," Cameron said in a televised speech in front of Downing Street following the referendum.

The final result showed some 55 percent of the voters rejected Scottish independence in Thursday's referendum.

Early this month, former British Prime Minister, pro-unionist Gordon Brown proposed a "timetable" to devolve more powers to Scotland over finance, welfare and taxation once the Scottish people reject independence.

In a rare non-partisan consensus, all three major parties in Britain, namely the Conservatives, the Labour party and the Liberal Democrats, have unanimously backed Brown's proposal.

Cameron announced that Robert Smith, Chairman of the Commonwealth Games Glasgow 2014 Organizing Committee, will oversee the fulfillment of the commitments.

Devolved powers over tax, spending and welfare for Scotland are expected to be agreed by November and draft legislation would be published by January next year.

"We have heard the voice of Scotland -- and now the millions of voices of England must not go ignored," he stressed.

In his speech, Cameron also vowed to have wider civic engagement in improving the country's governance, including plans to empower British cities.

Before the speech, he congratulated to Scotland's First Minister Alex Salmond on his hard-fought campaign.

"I'm delighted the SNP (Scottish National Party) will join talks on further devolution," Cameron said on his twitter feed.

Salmond conceded defeat in the referendum and urged the pro-union parties to honor their commitments of more devolved power to Scotland.

"I accept that verdict of the people and I call on all parties of Scotland to follow suit in accepting the democratic verdict of the people of Scotland," he said in a speech following the announcement of the "No" victory.

"The unionist parties made vows late in the campaign to devolve more powers to Scotland. Scotland will expect these to be honored in rapid force," the SNP leader urged.

British Deputy Prime Minister Nick Clegg, leader of the Liberal Democrats, said he was "absolutely delighted" that the Scottish people have taken this momentous decision to safeguard "our family of nations."

"The independence referendum has led to demand for constitutional reform across the UK. People want power in their own hands, not hoarded in Westminster," he said in a tweeter.

"In a dangerous and uncertain world I have no doubt we are stronger, safer, and more prosperous together than we ever could be apart," the deputy prime minister noted.

Ed Miliband, leader of the opposition Labour party, said the United Kingdom is "stronger today than it was yesterday," adding that he was delighted and proud that the people of Scotland have made this historic decision to stay.

British Queen Elizabeth II is also expected to make a written statement on Friday afternoon.