After Brexit will we really increase trade to the rest of the world? What stops us now?

We have a problem in the UK but I'm not sure it's connected with the EU although I realise many people will disagree with me.  However, take a look at the chart (HERE).  It shows figures from 2013, so not quite up to date but I think it will illustrate the point I am about to make.

In 2002 we were the fourth largest exporter to other EU countries with £182Bn but Holland, France and Germany were ahead of us.  Bear in mind Holland has a population of about 16 million compared to our 60 million or so but managed to export more than we did.

By 2013 our exports had dropped to £178Bn and we were sixth, Italy and Belgium overtaking us. Belgium has a population of about 11 million, roughly 20% of ours but exports more than we do.

These are all countries that are "shackled" or held back by EU red tape and regulations but seem to be doing very well.  The EU as a whole runs regular, large trade surpluses with the rest of the world  and it widened by 31% in 2016 to £24Bn per month.  On the other hand the UK runs a trade deficit of about £40Bn per year.

Even Poland, admittedly from a low base increased its exports from £35Bn in 2002 to £113Bn in 2013 while ours declined.  It is clear to me we have problems with productivity and exporting but I am not at all clear that it is connected with the EU.