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Scotland has voted No to independence, prompting a huge sigh of relief to echo through the corridors of Westminster. It means David Cameron has not gone down as the prime minister who lost the United Kingdom. He will not be forced out of office.

Ed Miliband has also not gone down as the Labour leader who lost Scotland to the nationalists. And Nick Clegg will not find himself working with a new prime minister.

But the political consequences of a No vote are huge. This is because Westminster has vowed to say yes to more devolution. The leaders of the three largest UK parties have promised that the Scots will get more powers over their taxes, welfare and spending.

They hope to agree the details by November and publish draft legislation in January. But it wil not be easy, not least because the parties disagree over detail.

Take taxation. The Conservatives say Holyrood should be able to set income tax rates and bands, with just the tax-free personal allowance decided by Westminster.

Who votes on what?

Labour says Scotland should be able to vary income tax only by 15 pence in the pound.

The Lib Dems believe the Scottish government should be able to fix not only income tax but also capital gains, inheritance and a whole range of other taxes. Somehow these differences will need to be hammered out - and soon.

But as well as securing agreement among themselves, Mr Cameron, Mr Miliband and Mr Clegg will have to win support for their plans from within their parties.

Many MPs are worried about what they see as rushed constitutional reform. Others are worried about the lack of consultation. And many Conservatives are asking why they should follow an agenda they believe is being set by former Labour Prime Minister Gordon Brown.

And there will be principled opposition by some MPs who think any more power for Scotland should come only with wider constitutional reform for the whole of the UK.

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Many Conservatives believe extra devolution to Scotland should be matched by giving English MPs a greater say over English laws. That could mean, for example, English MPs alone deciding the detail of legislation that affects England, with the whole UK parliament - including MPs from Scotland - deciding the broad principle.

Or it could mean English MPs having total control over English legislation, effectively sitting as an English parliament at Westminster for a couple of days a week.

And Tory MPs will be in no mood to compromise. Many blame the prime minister for putting the Union at risk by the way he handled the referendum and the campaign. They are also unhappy at the haste in which Scotland was offered so much in a desperate attempt to stave off independence.

Giving English MPs greater powers would open up another constitutional can of worms. Labour would be hugely cautious, and not just because its Scottish MPs would resist any loss of influence at Westminster.

Labour would be concerned that if it was elected to government in the future, it could end up with the ability to declare war and agree treaties but not get its domestic budget through Parliament if it had no English majority.

There will also be demands for change elsewhere in the UK. In Wales, there have already been concerns raised that fixing Scotland's public funding formula - as the leaders have vowed - would mean no extra money for the Welsh.

Wales has long complained at what it sees as the unfairness of the so-called Barnett formula which it says is generous to Scotland but less so to itself.

And in Northern Ireland there will be more calls for Stormont to win control over corporation tax, and even more demand for extra resources to relieve the pressure on parties deeply divided over budget cuts.

So the details of this are complicated, the politics tricky and the potential for disagreement huge. But the pressure on the UK parties to deliver will be immense.

If they succeed, then this process would become a catalyst for radical constitutional change that could transform UK politics for the 21st Century. But if they fail the potential breach of public trust would tarnish Westminster's name for good.