Murdo Fraser has called for the House of Lords to be abolished after Brexit and replaced with a Senate with elected members from across the UK.
The Tory MSP made the call in a paper for the Bright Blue Scotland think tank, which recommended a “quasi-federal” settlement to save the Union.
The paper argued that the current political arrangements are inadequate and support for independence in different parts of the UK will increase unless there is constitutional reform.
Mr Fraser said: “With nationalists in different parts of the United Kingdom seeking to use Brexit uncertainty for their own political ends, it is important that unionists have a coherent response.
“Introducing a UK-wide Senate delivers the long-awaited and overdue reform of the House of Lords, giving a better balance to the UK constitution and protecting the interests of the nations and regions furthest from London.
“A new quasi-federal settlement can mitigate concerns that exist in Scotland, Wales and Northern Ireland, and also are growing in many parts of England.
“These are about an over-centralised state where, despite asymmetric devolution over a period of two decades, there is still pressure for more power to be passed down from the centre.”
The report argues the House of Lords should be abolished and replaced with a new Senate, or Upper House, representing different parts of the UK.
This should be predominantly – if not entirely – elected, fulfilling the role both of a revising chamber and as a counterweight to the Commons.
It calls for a new Statute or Charter of Union, which would declare the creation of a quasi-federal state and provide legislation for the UK’s intergovernmental work.
Ryan Shorthouse, director of Bright Blue, said: “Notwithstanding the difficulties and divisions Brexit has created, it does offer an opportunity for overdue democratisation and modernisation of key institutions of the union.”
SNP MSP Tom Arthur said: “Even the Scottish Tories now admit that support for independence is on the rise because of the way Scotland has been utterly ignored throughout the Brexit process.
“Murdo Fraser’s comments show the Scottish Tories are rattled.
“They are running scared of independence because they know that recent experience of a broken Westminster system will only lead more people to support Scotland taking its own decisions.”