The simple answer to Skidelsky's question

Increased automation leads to greater productivity of labour, this is true. This means that we need less labour to achieve any one task, we therefore have labour available to tackle a further such task. The end result being that we now undertake, or perform, two tasks with our available labour and so are richer - we’ve the two, not the one, things.

So far so good then Skidelsky goes wrong:

The problem is social: to ensure that the fruits of increased productivity are passed on to the mass of the people in the form of higher wages and non-work income. The political debate is about how much public intervention is needed to ensure that the wealth created by machines trickles down to all sections of the population.

This is to make the mistake of thinking that your income is the amount of money received for your labour. Not so, your real income is what you are able to consume as a result of your labour. As society is now more efficient in its use of labour, more is being produced that can be consumed, therefore real incomes have risen as a result of the increased productivity.

This doesn’t in fact require public intervention. It’s a natural outcome of a market economy. That increased production hits the supply and demand curves, prices fall, consumers benefit.

The mistake is to think of the benefits from automation arriving to us in our roles as workers - they arrive to us in our roles as consumers instead. As William Nordhaus memorably pointed out, 97% or so of the benefits of entrepreneurial innovation - not exactly the same as automation but not far off it either - arrive as the consumer surplus. This being achieved simply though market competition, no politics nor public intervention required.