In an interview with the BBC, Mr Corbyn said he wanted a constitutional convention to improve representation for English regions and iron out differences between the powers of devolved assemblies, but failed to back Ms Dugdale’s initiative. The Scottish Labour leader unveiled her blueprint for the future of the Union last month, saying the relationship between Scotland and the UK needed to be overhauled to prevent the fallout from Brexit “breaking the Union once and for all”. But despite agreeing with the outline of Ms Dugdale’s proposal, the UK Labour leader questioned the language she used to launch her plan, saying: “I wouldn’t use the words ‘new Act of Union’”. “I want us to look at the constitutional relationships,” Mr Corbyn said. “What we’ll be looking at is a new constitutional convention for the whole of the UK, because there are issues of lack of democracy in parts of our political structure, such as the unelected upper chamber, the House of Lords.” Asked about the likelihood of a second referendum on Scottish independence, Mr Corbyn said a vote should be held if a majority of MSPs agree. “I wouldn’t ask for one, although quite clearly if the Scottish Parliament wanted to have one the agreement has been that a second one could be held,” he said. “I think it’s much more important that we address the economic issues facing the whole of the UK, and of course the negotiations with the European Union about what form of relationship we have with Europe in the future.” The interview, in which the UK Labour leader admits he has failed to keep a promise to visit Scotland every month, is the latest indication of the sometimes difficult relationship between Mr Corbyn and Ms Dugdale. A bitter power struggle played out at the UK Labour conference in September as Mr Corbyn’s allies tried to block party reforms giving the Scottish Labour leader a seat on the powerful national executive. Labour’s only MP in Scotland, Ian Murray, resigned as shadow Scottish secretary before being given a role in Ms Dugdale’s front bench team. SNP MSP Ivan McKee MSP claimed it was a “complete and utter embarrassment” that Ms Dugdale’s plans for the constitution had been “fatally undermined” by her own leader. “Just last week Kezia Dugdale claimed that her London leader was backing her all the way, and that he supported her plan ‘unequivocally’,” he said. “But it’s now clear that nothing could be further from the truth. “It’s one thing for Scottish Labour proposals for a ‘new Act of Union’ to be ridiculed and trashed by opponents, but quite another for them to be kyboshed by Jeremy Corbyn himself.” Scottish Conservative leader Ruth Davidson said: “I never thought I’d find myself agreeing with Jeremy Corbyn. “But he’s quite right to reject the idea of a new act of union; it’s clearly little more than a Scottish Labour gimmick, from a party all at sea on the constitution. “Instead of constant flip-flopping on the issue, Labour should be standing full-square behind Scotland’s decision to stay part of the UK.” A Scottish Labour spokesman said: “Labour will not support another independence referendum. More than two million people in Scotland voted to remain in the UK and that vote should be respected. “Kezia Dugdale has proposed a new Act of Union, to strengthen our union across the whole of the UK for generations to come.” Mr Corbyn also rejected calls from the Scottish Government for immigration powers to be devolved as part the Brexit settlement. The Scottish Affairs Committee and a cross-party group of MPs looking at social integration have both backed the idea of nations and regions getting more power over immigration. However, Mr Corbyn said any such moves would result in border checks within the UK. “It would be very difficult to have regional immigration policies because if you have regional immigration policies, presumably you would have to have regional borders,” he said.