The 6th Duke of Westminster, who died this month, was living support of the claim that wealth doesn’t make you happy. He was as rich as can be, but said he wished he hadn’t been. The dukedom, and the billions of pounds it brought with it, came to him unexpectedly. He had been brought up on a farm in Northern Ireland and wished he had stayed there and become a beef farmer. Instead, he inherited a great property empire in England and around the world, as well as various estates that allowed him the pleasure of game shooting, but otherwise gave him little but grief.

He was overwhelmed by the onerous duties that great riches imposed on him, and he succumbed to depression. ‘Given the choice I would rather not have been wealthy, but I never think of giving up,’ he once said. ‘I can’t sell it. It doesn’t belong to me.’ He could have just run away from it all, I suppose. But the heads of ancient noble families tend to feel an obligation to take care of their inheritance for future generations, and Gerald Grosvenor was one of those. He came into the dukedom at 28, and it seems thence to have blighted the rest of his life.

There are certainly some disadvantages in being very rich. It makes people isolated and treated warily by others. And they don’t have many pleasures that are denied to the merely comfortably off — only yachts, aeroplanes, and the like — and, as Frank Sinatra sang in High Society, who wants those? Nevertheless, there are few people who wouldn’t rather be richer than they are at the moment and thus be spared from the worries that shortage of money can cause. Surveys have shown that most lottery winners have been made happier by their sudden wealth, however much we would like to hope the contrary. They are relieved from financial anxiety and can afford to do things they have never been able to do before. They can also, if they are so disposed, give money away.

The late duke was a generous philanthropist, mainly to military veterans, farmers and countryside campaigners, though not to an extent that would have impinged much on the size of the family’s pile, and not on the scale of some American billionaires. There are some, like Donald Trump, who are very sparing with charity, but Bill Gates, Warren Buffett and Mark Zuckerberg have been spectacular with their generosity.

Zuckerberg and his wife have pledged 99 per cent of their Facebook shares, valued last year at $45 billion, to a charitable organisation they have founded to support health and education, while Gates and Buffett have joined forces to commit most of their fortunes, worth about $60 billion, ‘to reduce inequities and improve lives around the world’. They have even demanded that the mega-rich should pay more in taxes.

You couldn’t imagine British billionaires doing the same. Gates and Buffett won’t leave their children poor but, as Buffett said about his own, they should have ‘enough money so that they would feel they could do anything, but not so much that they could do nothing’. They are inspired to some extent by the American ideal of a meritocratic society, in which everyone starts with the same opportunities and that no hereditary ‘aristocracy’ is allowed to emerge; and they probably also agree with Andrew Carnegie ‘that huge fortunes that flow in large part from society should in large part be returned to society’.

British billionaires tend not to feel like that: think of Sir Philip Green. They are also loath to admit that luck has played any part in their achievement, whereas Buffett has said that he got rich not ‘because of any special virtues or even because of hard work, but simply because I was born with the right skills in the right place at the right time’.

The Duke of Westminster was acutely aware that his own vast wealth was entirely due to luck. When once asked for the secret of financial success, he replied it was to have an ancestor who had been a close friend of William the Conqueror. It may have been that his inability to know how to make amends for this fluke lay behind his discontent.