The move comes despite calls from the Government and businesses to strike a data sharing deal, amid claims that the UK’s £240bn data economy could "fall off a cliff edge".
It is not known whether Barnier's remarks will have an impact on the UK's aim of achieving so-called "data adequacy" status, which is granted to countries that are not part of the EU but whose laws are aligned to the EU’s standards.
Currently ten countries have been granted the status, including Israel and New Zealand. The USA and Canada have only been deemed to be partially adequate.
However, the UK Government was actually demanding more. Prime Minister Theresa May recently said: "We will need an arrangement for data protection. The UK has exceptionally high standards of data protection. And we want to secure an agreement with the EU that provides the stability and confidence for EU and UK business and individuals to achieve our aims in maintaining and developing the UK’s strong trading and economic links with the EU.
"That is why we will be seeking more than just an adequacy arrangement and want to see an appropriate ongoing role for the UK’s Information Commissioner’s Office. This will ensure UK businesses are effectively represented under the EU’s new ‘one stop shop’ mechanism for resolving data protection disputes."
On this last point, Barnier was in no doubt, he said: "It is the United Kingdom that is leaving the European Union. It cannot, on leaving, ask us to change who we are and how we work. The United Kingdom wants to leave. That is its decision. Not ours. And that has consequences.
"Let’s be clear: Brexit is not, and never will be, in the interest of EU businesses. And it will especially run counter to the interests of our businesses if we abandon our decision-making autonomy. This autonomy allows us to set standards for the whole of the EU, but also to see these standards being replicated around the world.
"We cannot, and will not, share this decision-making autonomy with a third country, including a former Member State who does not want to be part of the same legal ecosystem as us."