If this were true it would most certainly be undesirable:

We spend so much time talking about this titanic clash between the free market and the social state – yet ignore the fact that most of our major "markets" no longer operate as such. This is an oligarchy whose only governing authority is the administrator of wrist-slaps, and whose principles begin and end with the preservation of its jointly and severally managed profit. Which is to say that they're not competing against each other; they collaborate brilliantly – which would be sweet to watch were it not for the fact that they are working together the better to screw us.

Monopolies and oiligopolies are indeed undesirable things. And we here at the ASI spend much of our time pointing this out and arguing for the one known solution to the problem, more markets, more free markets. But what really surprises is the example that Ms. Williams uses to bolster her case:

Looking specifically at PPI, we could also see the counter-intuitive but obvious point that banks aren't charging enough for their services: current accounts cost money to administer. But rather than admit this, they would prefer to outwardly compete with one another, vie to see who can be the most free, while recouping the money by sleight of hand (swingeing overdraft charges), irresponsible lending or outright cheating (mis-sold PPI). This is what a market with only four or five big players looks like: amazing value in the top line, all the profit draining from somewhere you can't see.

In a truly competitive market we expect profits to decline to something around zero. In the long term perhaps to the level that just covers the cost of capital: something the UK commercial banks do not manage. In the proper economic sense they are therefore losing money: just the result we expect from that truly competitive market.

So, in the provision of current accounts we have evidence that we do indeed have that desired competitive market. Yet this is being taken as evidence of oligopoly? What is it they're putting in the water over there in York Way?