This was disproven a couple of weeks back. The deals currently in place we signed as a sovereign country, just like all the other countries signed it. It was not signed between the EU and whoever because the EU is not a Sovereign nation as yet. The legal people have already said that the agreements we have signed will remain in plain whether in or out of the EU.
The deals with the USA, China, India have been going on far longer than GOT has existed and are still not in place. The UK on it's own and not part of a 28 group committee (which wasn't even 28 when talks started, so the goalposts always move) would have easily concluded such deals before now.
In respect of EU competition for trading partners, we will still be competing against France and Germany just as we do today..........
		
		
	 
The Head of the WTO reckons otherwise according to the Guardian.
https://www.theguardian.com/busines...rexit-trade-talks-start-scratch-eu-referendum
Negotiations about the shape of the UK’s post-Brexit trade arrangements would have to start from scratch after a leave vote in the 
EU referendum, the head of the World Trade Organisation said as he admitted there had been no preliminary discussions with the UK government.
Roberto Azevêdo, the 
WTO director-general, said he expected any talks to be long and difficult, adding: “We haven’t had any discussions about the process. We don’t know what the process would be. We do know it would be a very unusual situation.”
Trade has featured heavily during the referendum campaign, with much debate about whether a post-Brexit UK would seek to retain its membership of the European single market or aim for a looser arrangement in which exporters had the same access as other WTO members.
Azevêdo said the position was complicated by the fact that all Britain’s trade commitments had been negotiated by the EU and that these would cease to apply in the event of a decision to leave.
Warning that it would be impossible for the UK to “cut and paste” its old EU trade deals into new agreements, Azevêdo said the UK would be starting from scratch without the institutional machinery necessary to negotiate trade deals.
He said Britain did not have the investigative bodies that would look into issues such as steel dumping. “It doesn’t have the official capacity. There is no institutional mechanism to conduct an investigation. That body of human resources would have to be set up fairly quickly.”
Azevêdo said he felt “uncomfortable” being dragged into the UK’s referendum debate but thought it was right to counter a great deal of misinformation about the UK’s future as a WTO member. He said there had been no pressure on him from the government to speak out.
“Britain is a member of the WTO and will continue to be a member of the WTO. But it will be a member with no country-specific commitments. We have had no other situation like that,” he said.
One of the leading figures on the leave side, 
Prof Patrick Minford, has said Britain could avoid protracted negotiations by adopting a free trade approach, under which the UK would impose no barriers on goods and services entering the country. Minford said this would help the economy by making imports cheaper.
Azevêdo said this would be an all-or-nothing approach: “If you are a duty-free country, you can’t be selectively duty-free. If you want to go duty-free, you have to go duty-free across the board. There can be no tariffs on anything, including agriculture and steel.”
The WTO director-general has been seeking reductions in protectionism from member countries as part of his organisation’s mission to promote free trade. He said: “If everybody went in a duty-free direction it would be a golden time for classical and orthodox economics.”
Noting that only Macau and Hong Kong adopted a complete duty-free approach, Azevêdo said: “I recognise reality for what it is. I think it is very unlikely it (a duty-free world) is going to come to pass.”
Azevêdo, who has been struggling to bring to a conclusion the 
Doha round of liberalisation talks which began in 2001, said he had no idea how long it would take the UK to negotiate trade deals afresh in the aftermath of a leave vote.
“It is very difficult to predict. Russia’s accession to the WTO took 20 years. Other negotiations happened faster. It will be a very high risk bet to hope that negotiations would be quickly completed and that negotiations would be uneventful,” he said.