However, from its creation in 1969 until the Higher Education Acts of 1992, the Open University remained outwith these arrangements.
The government rightly believed that the funding of a radically different university was unlikely to be handled sympathetically by a University Grants Committee which had been established to serve more conventional universities. The OU was funded directly by the Department of Education and Science (DES).
Letting ministers decide the annual allocation of public money to the OU carried its own risks, as when accusations of political bias were levelled at some of the university's courses in the 1980s.
Nevertheless, the arrangement allowed the OU quickly to establish itself as the UK's largest university and the world leader in open learning. But by the end of the 1980s the OU had become too large a camel to fit comfortably in the DES tent.
Ministers found it increasingly difficult to translate the policies of the bodies that funded the rest of higher education into sensible decisions for the OU. So they took advantage of their reforms of 1992 to include the OU in new funding arrangements.
These reforms brought in two other changes. First, the polytechnics were granted university status, creating a much larger university sector. Second, the pan-UK funding bodies were replaced by separate funding bodies in each home country: England, Scotland and Wales.
How would the OU, which operated across the whole of the UK, fit into this scheme? The 1992 Acts chose an evolutionary approach. They provided, in principle, for the OU to be funded, for its operations in each country, by the English, Scottish and Welsh higher education funding councils respectively.
The government also agreed, however, that for the time being the English funding body would be the channel for funding the OU for its activities across the whole of the UK.
It was predictable that the separate funding bodies would take the power devolved to them and develop their policies for supporting higher education in different ways.
This meant that the OU had to operate in Scotland under funding priorities devised for England, even though the priorities of the Scottish Office were somewhat different. But we muddled through.
The creation of a Scottish Parliament changes the context completely. In anticipation of today's elections the government acceded to the OU's request to move its funding for Scottish students to Scotland.
Now that higher education policies for Scotland will be determined by the democratically elected representatives of the people of Scotland, the Open University wishes to be integral to the implementation of those policies. As the UK becomes a federal structure the OU will evolve with it.
The emergence of a federal structure will not be straightforward, either for the UK or for the OU. Federalism is a product of reason in politics, born of a decision by pragmatic politicians to face facts as they are, notably the heterogeneity of our population.
It is an attempt to find a rational compromise between divergent interest groups - but a compromise based on the will of the people.
Comparative research across the cantons of Switzerland shows a solid positive correlation between human happiness and the extent of direct democracy.
If this proves true in the UK, then no doubt people in Wales and in the various regions of England will follow the example of their happier compatriots in Scotland and take greater control over their affairs, including their academic affairs.
Meanwhile the Open University will try to give excellent service to all citizens of the UK within a mixed polity. We shall take advantage of our international scale to develop courses of quality for people everywhere.
But we shall adapt and support those courses to fit the policies determined by each electorate. It will require us to "think globally and act locally" but also to think locally and act globally. It is an exciting prospect.