One British household in every 10 now has total assets exceeding £1m, according to a new book based on work by researchers at the London School of Economics. A surge in stock markets, London house prices and the valuation of occupational pensions will "have pushed the entry point into that wealthiest tenth over the million-pound mark today", says Prof John Hills, the lead author.

Hills – who previously headed Whitehall's National Equality Panel – points out this is real money, and a little bit of it will be used to secure an extra social advantage for the offspring of the tenth who now are so wealthy. It will pay for that master's degree, or the deposit on their "starter" home.

That will have the effect of reducing social mobility because educational attainment will begin to depend more on having parents who can pay, and being able to take that good job in London will depend on having parents who can help you buy a place to live should you wish to stay in the job for long.

So why are house prices so high? It is not, as often suggested, because we have too few homes. Prices are high because a few have so much more money to spend than before. They buy a big house for a small family, or more than one home, and reduce what is available for everyone else.

And why do you think parents are so frightened about their children's futures? It is not because our schools are poor. We've never had so many well-qualified and committed teachers working per child, and we have never had so many university places available per child. But we have also never had such a premium placed on getting into the "right" school, or such a high fee charged for getting into university to supposedly secure that higher-paid graduate salary .

If the gap between graduate salaries and non-graduate wages had not widened so much in recent decades do you think it would be possible to persuade students to sign up to such enormous debts just to be allowed to study at university? Do you think people would pay such a premium to live in the "right" school catchment area? Parents are instilling in their children the belief that only by having and spending money can you secure your leg up in the employment race. Would teenage levels of anxiety be as high as they are now if inequalities in income and wealth were lower, and would adult levels of mental health improve if inequalities were to fall?

And why are so many young people unemployed? Our overall wage and salary bill has never been higher. It is not that we don't have enough money to employ them. If fewer people were allowed to hoard so much wealth, and those at the top were paid a little less than they currently are, it is not hard to calculate that everyone aged under 25 without a job could have one, full-time paid at the living wage.

So, what is to be done? Rising inflation will eat away at the wealth of the rich. Housing bubbles all burst, eventually, it is just that no one knows when the London crash will begin, but one day someone will calculate the cost of a square foot of land in Kensington and work out that even if it were tiled in gold it would not be worth this much. Then they will buy some gold instead of that apartment, and theirs will be the very first decision of many that will bring us a little nearer together again.

At some point the bubble in "top-talent" salaries and bonuses will burst too. It did before, in the years after the 1929 crash, but it has been so long that we have forgotten such things are possible. We have also forgotten that the gap between rich and poor fell almost every year for a further 50 years after that last crash. Income and wealth inequalities narrow as well as rise.

Agitation helps. For example if Scotland were to gain independence there would be costs. Those best placed to meet the additional costs are the richest tenth of landowners in the country. Scotland could become a more equal country in the near future and a great deal of the debate on Scotland will soon turn to that possibility. What effect will such talk then have in England?

What will matter most is what we really believe in our heart of hearts. As David Cameron said, in 2009: "We all know, in our hearts, that as long as there is deep poverty living systematically side by side with great riches, we all remain the poorer for it". For people without great riches, they don't just know it, they live it. And as voters in Scotland begin to seriously debate whether another path is possible, such ideas could become contagious.

• This article was amended on 23 May 2013. It originally misspelled Prof John Hills' surname as Hill in the second paragraph. This has now been corrected.