Failing to comply with demands from Brussels could lead to infraction proceedings brought by the Commission and infringement actions by member states, according to UK press reports.
If such legal proceedings were brought against the UK, it would be "required to pay a fine."
The revelations, detailed in the UK media, come in the wake of Friday's EU summit on the future of Europe in Bratislava, the first without a UK Prime Minister taking part for 40 years.
EU leaders issued a six-page, post summit statement, titled "The Bratislava Declaration", which pledges to reinforce Europe's external borders.
Media reports now say the UK could be fined millions of euros if it tries to negotiate trade agreements with other countries before leaving the EU.
Reacting to the revelations, UK MP Barry Gardiner, Labour's shadow Secretary of State for international trade, Europe, energy and climate change, laid the blame for such a scenario at the feet of the UK government.
He said, "It is precisely this mixture of arrogance and incompetence by Liam Fox that will cause major problems for the UK in our Brexit relations with Europe."
Fox, who supported the Leave campaign, is one of three senior Tory MPs tasked with overseeing Britain's Brexit negotiations with Brussels.
Gardiner said, "Fox seems to think he can just ignore the rules and that the EU will neither notice nor seek to retaliate in any way. Fox has a record of acting as if the rules do not apply to him.
"The Prime Minister must realise that if she wants to protect the UK's interest and secure a new relationship with Europe that protects access to the single market and controls immigration, then she must stop cavalier ministers like Fox from alienating the very people on whom our future relationship with Europe depends."
It has also emerged that the Scottish National party is reportedly seeking assurances from EU member states that an independent Scotland could remain in the single market after Brexit.
Senior SNP figures now also believe a second referendum on independence could be held by autumn 2018, before the UK leaves the EU.
The Scottish government believes the guarantee about the single market would ensure greater support for independence in a second referendum, and are working to persuade member states to let them be treated as a continuing member of the EU.
Meanwhile, European embassies in Britain have logged dozens of incidents of suspected hate crime and abuse against their citizens since the vote to leave the EU, according to new figures.
The vast majority of xenophobic incidents involved citizens from eastern European countries, with more attacks against Poles than all the other nationalities put together, the survey of EU embassies in London revealed.
The Polish consular service in London, Manchester and Edinburgh has logged 31 incidents of reported hate crime since 23 June, including eight attacks in the past three weeks.