Murdo Fraser has warned that without change, support for separatism will be "inflamed" in different parts of the UK including Scotland, in a new report today.
Plans to repatriate a tranche of new powers from the EU back to Scotland after Brexit - through Common Frameworks - have also come under fire from Mr Fraser, the Tory Finance spokesman.
Bright Blue Scotland published its report - Our still United Kingdom - putting forward new constitutional arrangements for the country following its EU departure.
The paper, authored by MSP Murdo Fraser, argues that current arrangements are inadequate and support for independence in different parts of the UK will increase if further reforms are not introduced.
“Our departure from the EU will require new processes, and structures, to be created within the United Kingdom," Mr Fraser said today.
"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. So it is time to reform our government structures to create a ‘quasi-federal’ United Kingdom.”
“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 Senate representing different parts of the UK would replace the House of Lords, representing different parts of the UK, predominantly if not entirely elected.
There would also be a new UK Council of Ministers would also be set up to manage relationships with the devolved nations of the UK, scrappnig the current joint ministerial committees.
A new English Grand Committee would also be set up to ensure England as a whole is represented in the new Council of Ministers.
Ryan Shorthouse, Director of Bright Blue, says: “Our departure from the EU provides the impetus to introduce important governmental and constitutional reforms to create a ‘quasi-federal’ future for the four nations of the Union.”
“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.
“That trend is only set to increase because the UK Tory Government has shown absolutely no sign it is prepared to listen to Scotland.
“Instead, they arrogantly insist that they know best, proposing to drag us out of Europe against our will, doing huge damage to jobs, public services and our economy.
“Murdo Fraser’s comments show that 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.”