The EU has formal responsibility for negotiating trade deals on behalf of all countries inside the organisation and expressly prohibits member states from negotiating separate arrangements.
The treaty on the functioning of the EU states: "The Union shall have exclusive competence in ... common commercial policy."
This means the UK is blocked from entering any kind of formal negotiation with other countries until those treaties no long apply - something which happens only after the UK has actually exited the EU, which follows a two-year negotiation period after Article 50 is invoked.
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"The legal position of the UK with regard to trade deals - and everything else - is unchanged at present," said Tamara Hervey, a professor of European law at the University of Sheffield.
Stephen Weatherill, a professor of European law at Oxford university agreed. He told City A.M.: "[It's] not allowed. Simple as that, as a matter of EU law."
"The UK has to respect its obligations under EU law," added Anzhela Yevgenyeva, a research fellow at Oxford University.
With European politicians lining up today to say that the UK remains a member of the EU - and the associated "rights and obligations" remain in force until it has formally untangled itself - there are also questions as to whether European officials would ease the rules and begin to allow the UK to negotiate with other countries - or whether the UK could ignore the rules and start negotiating anyway.
Allie Renison, head of Europe and trade at the Institute of Directors said there was "no way" the EU would let the UK start striking out into the world just yet, meaning we would still be blocked from talking to other countries "because it's breaching legal obligations".
She added: "There might be some legal room for informal discussions with countries the EU already has deals with to try to get a sense of whether those countries want to go on with that deal."
Raoul Ruparel, co-director of think tank Open Europe agreed that the UK might be able "to start informal talks and negotiations around potential trade deals," we "can't change tariffs or strike deals with anyone else".
He added: "But it's not clear how much progress this can make given we can't sign anything."
If the UK simply chose to ignore EU law and did try to go ahead and agree new deals, Oxford University's Yevgenyeva said "formal enforcement mechanisms [by Europe in response] might not be the most efficient route in this context, but in political terms, it might still bite" as the UK was made to pay in any negotiations about exiting the EU on good terms.
Renison said striking trade deals with completely new countries was in third place on the government's list of priorities, anyway, behind maintaining access to the EU and protecting or replicating the trade deals the EU has signed off on our behalf.
During the campaign, Barack Obama warned the UK would be at the "back of the queue" when it came to trade negotiations, given the strain on resources the process entails. However, writing for City A.M. James Paterson, a senator for Victoria in Australia's federal parliament said Australia couldn't wait to forge better ties with the UK after it has left the EU.
If the EU manages to conclude and ratify the Transatlantic Trade and Investment Partnership (TTIP) with the US before the UK formally leaves, then agreeing a deal on similar terms with the US could be easier for the post-Brexit government, Renison said.
Even if all the countries with which the EU currently has deals would like to extend them to the UK after it leaves, there is still the possibility of a gap.
"It's not necessarily because countries will want better terms, just legally, they will have to be redone," Renison said.
Professor Hervey added: "Unless we opt for a future relationship with the EU that is outside all the European frameworks then .... our ability to strike trade deals with countries will be affected by that future relationship."
The business secretary is holding a roundtable today for leading business figures where discussions on trade deals are expected to be one of the main talking points. Yesterday, David Cameron announced the creation of a "Brexit unit" made up of civil servants from across Whitehall to discuss options for a future relationship between the UK and the EU.
During the referendum campaign, the official Leave campaign said outside of the EU, the UK "will gain the power to strike our own trade deals, creating new business opportunities and creating more jobs."
It added: "We will negotiate a new UK-EU deal ... we will carry on trading with Europe but we will also be able to negotiate trade deals with other countries."