Then go north to Bloomsbury, to the British Museum, where is being created the finest new public space in the capital for many years. This is the Great Court Scheme, due for completion in 2000. An inner courtyard, of vast size and noble proportions, hidden from view since the middle of the last century, is being opened up to reveal the domed Reading Room. It will be the city's first covered square. I agree with the scheme's architect, Sir Norman Foster, when he says that "what I think we have found is not just a new heart for the British Museum, but a great new public plaza for London".
Finally, walk briskly north for 20 minutes or so until you reach Euston Road. Look to your right, where St Pancras station stands, and there, crouched alongside, is the brand new British Library building. It has taken longer to construct than some medieval cathedrals, and was finally opened by the Queen last Thursday.
These new buildings have been paid for in different ways. The Sainsbury extension to the National Gallery was financed by the family whose name it bears before Lottery money became available. The Sainsburys have also contributed handsomely to the Royal Opera House, and to the British Museum, where they are underwriting the new galleries for the African collections.
The British Library is by far the most expensive project, at pounds 520m, a sum almost entirely provided by the Government; however John Ritblat, the brilliant property entrepreneur, has paid for a gallery which will house the Library's finest treasures, and Pearson Group, owner of The Financial Times, has also given support.
The Royal Opera House, the Tate and the British Museum have employed the now classic formula of Lottery grant plus matching donations from private benefactors.
By the way, I calculate that the total cost of these five building projects amounts to pounds 967m. Even leaving out of account the Millennium Dome, this is an enormous sum of money. The 1990s will have been a vintage decade for constructing new cultural edifices in the capital city.
Yet in this statement lies paradox. The five institutions confront the same perplexity. They are rich in capital for building projects, yet poorly endowed in income. The British Museum, the National Gallery and the Tate have alike narrowly avoided having to charge entry fees for the first time. At the last moment, the Chancellor of the Exchequer made funds available. None has any significant funds of its own for acquisitions, so the collections have become static. The Royal Opera House, in a desperate move, has just demanded that its pounds 15m a year grant be doubled. But the most pressing case may be the British Library.
The British Library is not only the place where one finds the earliest manuscript of the complete New Testament, the oldest surviving Buddhist texts, the Lindisfarne Gospels, two copies of the Gutenberg Bible (the earliest full-scale work printed in Europe using moveable type), the Anglo- Saxon Chronicle, the Magna Carta, the first collected edition of Shakespeare's plays, and the manuscript containing the lyrics of the Beatles' single "I Want to Hold Your Hand"; it is also the United Kingdom's national library. It has been receiving a copy of every British publication since the Copyright Act of 1842. To access and to make available this vast store of knowledge, around 9,000 visits are made to the Library's reading rooms in a typical week, 10,000 items are consulted, 12,000 reproductions are made and 13,000 enquiries answered. Likewise over 76,000 requests a week for remote document supply are received, 46,000 searches of the Library's website are made, and 60,000 searches of the on-line catalogue conducted. It could be argued that it is the country's most important cultural institution.
The Library receives an annual grant of just over pounds 80m and there will be no increase for three years. It charges for its services where it reasonably can, so that the proportion of its spending covered by the government grant has declined from 88 per cent in 1974 to 73 per cent this year. None the less, the Library considers that it is now under-funded by pounds 8m a year, and that this gap is likely to rise quite quickly to some pounds 20m a year as the demands for its services - a statutory duty to meet - increase. That is why it is considering charging for access to its reading rooms, at a rate of perhaps pounds 300 a year for regular users. This would break a 250-year-old tradition. Neither Karl Marx nor George Bernard Shaw paid to consult the Library's volumes.
Now turn to the Royal Opera House again. Unlike the British Library and the others, it is not central to one of the nation's cultural activities. The musical life of the country would not be unduly damaged if there was no Royal Opera House. I say this although I have greatly enjoyed many performances there. Its point of distinction is that, if properly funded, it can employ the world's greatest singers and lay on sumptuous productions, whereas the English National Opera, just down the road at the Coliseum, does not do so, although it attains high standards.
But also compare the Royal Opera House's demands with the value of a quite different musical initiative announced a few days ago. Chris Smith, the Secretary of State for Culture, has set up a Youth Music Trust which will be given pounds 10m a year of Lottery money to improve music teaching in schools. Mr Smith's long-term aim is to ensure that any young person anywhere in the country who wants to play an instrument will have the opportunity to do so. That would be a crucial development.
Everything about the Royal Opera House seems out of proportion. Its new building is more costly than either the Tate or British Museum schemes, yet the number of people who will benefit from the new facilities is much smaller - perhaps a tenth of the 6 million a year who visit the British Museum. The extra grant it has requested could be used in a more culturally enriching fashion for the nation if spent by, say, the British Library in avoiding charges for access to its reading rooms and restoring its services to what it considers to be a minimum level of effectiveness. Many other institutions, too, could make a better argument.
Later today Sir Richard Eyre's report on the Royal Opera House will be published. I hope it won't make a case for special treatment. Unlike the other cultural institutions I have mentioned, the Royal Opera House is marginal, truly the odd one out of the five.