“I think it important to keep that question open and on the agenda,” Vestager tells the Daily Telegraph, “we are not there yet but it is important to keep an awakened eye.”

The breaking up of Google has been on the European agenda for some time. Four years ago the European Parliament debated the issue.

Vestager makes the point that Google could become so big that it is indispensable to the economy.

Last year the EU fined Google £2.1 billion for favouring its own shopping services over rival shopping services in search results.

With a 90% share of European searches, Google has to avoid the legal consequences of abusing a dominant market position.

Europe has never broken up a company under abuse of monopoly law but, America, which invented competition law with the 1890 Sherman Act, has used abuse of a monopoly as a reason to break up AT&T and Standard Oil.

Since the fine for favouring its shopping service, Google has been hit with two more legal actions from the EU – for monopoly abuse in Android mobile software and AdSense advertising