The Claim of Right and the idea of a Constitutional Convention grew out of the Campaign for a Scottish Assembly (CSA), a pressure group established in the aftermath of the failure to secure a devolved Scottish Assembly in 1979. The CSA was an organisation of individuals committed to some form of Home Rule for Scotland that by the late 1980s came to argue that a convention was the way forward to secure such.
Various organisations participated, such as the Labour Party, the Liberal Democrats, the Scottish Green Party, the Scottish Trades Union Congress, the Small Business Federation, the Church of Scotland, as well as the other major churches, and other various bodies representing other strands of political opinion as well as civic society in general. Initially the Scottish National Party (SNP) participated, but the then party leader Gordon Wilson, along with Jim Sillars decided to withdraw the SNP from participation owing to the convention's unwillingness to discuss Scottish independence as a constitutional option.
The Tory government of the day were very hostile to the convention and challenged the local authorities right to finance the convention, although the courts found that they were in fact entitled to do so.