A 55 percent majority of Scots rejected independence on Thursday but the future political structure of the United Kingdom is still in doubt. If Scotland gets additional autonomy, as promised, the remaining three parts of the island nation may expect the same.

With 3.6 million Scots turning out to vote in a referendum that Alex Salmond, the Scottish National Party leader, had described as a “once in a generation, perhaps even a once in a lifetime opportunity,” the result was decidedly in favor of keeping the union with England, Northern Ireland and Wales.

Prime Minister David Cameron, who had urged the Scots to vote against secession, said he was “delighted” with the outcome and there should be “no disputes, no reruns.”

Before the referendum, Cameron and Britain’s other two major party leaders — Labour’s Ed Miliband and the Liberal Democrats’ Nick Clegg — had pledged to devolve more powers to Scotland if it rejected independence, including the ability to raise revenue and shield the National Health Service in the region from cuts or reforms enacted at the national level.

On Friday, Cameron said increased autonomy for Scotland should be part of a new constitutional arrangement for the whole of Britain. “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,” he said.

Some English lawmakers, including members of Cameron’s own Conservative Party, are dissatisfied with the promise to maintain a financial arrangement under which Scotland gets a disproportionate share of the national budget. They also complain that Scottish lawmakers in the House of Commons are able to vote on legislation that only concerns England and other parts of the United Kingdom but English lawmakers have no say over Scottish affairs.

This “West Lothian Question” — named so because it was West Lothian representative Tam Dalyell who first raised the issue in 1977 — might only come to be seen as more unfair when Scotland gets its own pension regime and own welfare policies. It already controls education and, to a large extent, health care.

Some English politicians argue that the solution is a separate English parliament. One downside of that, as David Downing argued at the Atlantic Sentinel this summer, concerns English dominance. “England has a population of fifty million compared to just over sixty million for the entire United Kingdom,” he pointed out. “An English parliament would therefore be in permanent competition with an overarching federal Westminster and also potentially be deemed more important to satisfy than those in other devolved areas of the country.”

One way to get around this, Downing suggested, would be to split England up into smaller regions and give those their own assemblies.

Some might say that this process was started with the granting of a London Assembly to the capital which alone has a population of some eight million. Historical regions such as Anglia, Mercia, Northumbria and Wessex could be templates for such a division. They would have similar population counts and be unable to compete with Westminster in their own right.

But that would entail a far more radical revision of the United Kingdom’s political structure than is contemplated by most leaders.