What you do, simply, is convince enough of those other social groups that their interests are best served by throwing in their lot with you than by supporting the other side. This is what it means to achieve ‘hegemony’ (leadership) within a wider ensemble of social forces.
This is a view which some might call vaguely ‘Marxist’, but which might more accurately be called simply ‘sociological’, because it is perfectly possible to endorse this view while remaining very sceptical about many analytical and political assumptions of most of the Marxian tradition
The leaders of the Labour Party have always rejected any kind of political action (such as industrial action for political purposes) beyond the framework and conventions of the parliamentary system. The Labour Party has not only been a parliamentary party; it has been a party deeply imbued by parliamentarism.