If I'm not mistaken UK is one of the larger economies, and therefore should have more influence over the negotiations than there smaller, and less significant countries.

As for free movement of things, I believe it is in the best interest of the EU to allow lenient trade with UK, insofar as it doesn't damage its reputation as a legitimate institution.

However if reputation does take precedence over economic sense, then the UK has plenty of other new opportunities, on a global scale, negotiate trade freely with little EU intervention.