The EU has reportedly threatened to impose economic sanctions to prevent Britain from undermining the bloc's economy after Brexit.
The proposals are aimed at ensuring a "level playing field" is retained once Britain leaves the union, with officials in Brussels worried the UK might slash tax rates and cut red tape in a bid to attract investment after March 2019.
The suggestions, which were published by the European Commission in a strategy paper this week, include putting Britain on tax blacklist of non-cooperative countries and imposing penalties on companies that receive state subsidies.
The news comes amid reports that Theresa May's advisers are secretly considering the possibility of striking a customs union deal covering trade in goods with the EU.
According to the Financial Times, senior British officials argue the move would limit a loss of trade with the bloc after Brexit.
The report, however, was swiftly dismissed by Liam Fox, who claimed being part of a customs union would not allow Britain to set its own regulations.
"It is very difficult to see how being in a customs union is compatible with having an independent trade policy because we would therefore be dependent on what the EU negotiated in terms of its trading policies and we'd be following behind that," the international trade secretary told Bloomberg.
Fox, who along with Theresa May has spent the last three days on a business trip to China which concluded on Friday (2 February), added: "We have to be outside of that to take advantage of those growing markets. One of the reasons we are leaving the European Union is to take control and that's not possible with a common external tariff."
While in China, May revealed that £9bn (€10.2bn) of business deals had been signed, but it is the trade with the EU that is causing the most concern.
The PM added: "What I favour is a deal, an arrangement for trading with the European Union which is going to be good for trade between the UK and the European Union and good for jobs in Britain."
May also said that she will not sack the Conservative minister who claimed that the civil service had been deliberately producing negative reports on Brexit.
During question in the House of Commons, Steve Baker, a minster in the Brexit department, made the suggestion that the leaked civil service reports were written in a "deliberately" negative way.