British Prime Minister David Cameron insisted on Sunday that further devolution promised to Scotland could not leave England "overridden", as initial relief over the Scottish people's decision to reject independence gave way to squabbling over powers.

Cameron tied greater Scottish autonomy to more English autonomy, saying the "fundamentally unjust" situation whereby Scottish MPs in the British parliament could vote on matters affecting only England could not persist.

English MPs have no such influence over the same issues affecting Scotland -- including health and education, because they are already controlled by the Edinburgh assembly.

Cameron said there was a "basic unfairness at the heart of our democracy" which had to be addressed.

In Thursday's historic referendum in Scotland on the 307-year-old union with England, Scots voted by 55 percent to 45 percent to stay in the United Kingdom, rejecting independence.

Jolted by one opinion poll which put the pro-independence campaign ahead just a fortnight before the vote, Cameron, along with other leaders from the two other main British parties, promised a swift package of further powers devolved to the Scottish parliament if Scots stuck with the UK.

But within hours of the result, Cameron suggested that greater Scottish autonomy must be matched by greater English autonomy, something hitherto unannounced.

Writing in The Mail on Sunday newspaper, he said the issue could no longer be ignored.

Cameron said while new powers over tax, spending and welfare were on their way to the devolved Scottish Parliament in Edinburgh, the rest of the UK was asking why they could not have the same.

"Why should Scottish MPs be able to vote on what is taught in English schools, to reduce spending on English hospitals, or even vary English or Welsh income taxes, when under the new settlement English or Welsh MPs would have no say in such matters in Scotland?" Cameron wrote.

"It is fundamentally unjust to have the views of the people of England and Wales overridden in this way."

The Conservative leader said any post-referendum settlement had to be fair and lasting.

"Forcing English people to accept policies on schools, hospitals and taxes for which they have not voted is not fair and such a settlement could not last," Cameron wrote.

'No ifs, no buts'

The matter threatened to overshadow the main opposition Labour Party's conference, due to begin Sunday.

Labour, which holds 40 of the 59 Scottish seats in the 650-member British parliament, wants further Scottish devolution to be separate from wider reforms.

Cameron, whose party holds just one seat in Scotland going into the May 2015 general election, issued a direct challenge to his Labour counterpart Ed Miliband.

"Either resolve this issue with us, or explain to the people of the rest of the UK why they shouldn't have the same powers," he said.

But Cameron's moves have earned stiff criticism from his deputy prime minister, the Liberal Democrat leader Nick Clegg.

Writing in The Sunday Times newspaper, the head of the junior party in Britain's governing coalition insisted there could be "no ifs, no buts" about delivering the hastily-agreed extra powers promised to Scotland, and the package "cannot be made contingent on other constitutional reforms".

"Surely we haven't fought to save our union in a vote north of the border, only to see it Balkanised," he wrote.

Queen Elizabeth II has led calls for unity in the wake of the referendum, while the Church of Scotland was to hold a service of reconciliation on Sunday.

Eleven people have been arrested after trouble flared in Glasgow, Scotland's biggest city, when crowds gathered following the referendum outcome.

Police had to separate rival pro- and anti-UK groups.

Meanwhile membership of the Scottish National Party, which controls the devolved Scottish Parliament and led the push for independence, has surged from 25,000 to 30,000 since the referendum defeat.

SNP leader Alex Salmond, Scotland's first minister, announced his intention to quit both roles following the result, but insisted: "the dream shall never die".