Not true. The supposed implication is that the EU is more dependent on us than we are on them. The problem with this analysis is that it ignores the difference in size between the EU’s economy (nominal GDP about £10 trillion in 2015) and the UK’s economy (nominal GDP about £3 trillion in 2015). It is the relative importance of trade to each side, not the absolute value of that trade, that matters. Evidence
About half of the UK’s exports go to other EU countries, amounting to about 14% of our GDP. Evidence
By contrast, only about 3% of the EU’s GDP is accounted for by trade with the UK. The rest of the EU is far more important as a trade partner for us than we are for them — which suggests the opposite balance of power in negotiations. Evidence
Another negotiating difficulty for the UK would be the fact that we had just voted to walk out on our neighbours. It would be hard to see where the requisite goodwill would come from for a favourable trade deal.