Unlikely. Sure you won't be as integrated with the EU, but that itself can give you some leverage over it. Whether the UK's in the EU or not, it's going to want the UK's money to continue functioning, and will be willing to give special concessions to make sure that happens.
The thing is, we have a model for this in Norway, who trade in the EU and have to comply with the rules for many things. They have no vote on the rules which are passed but have option to ignore some things. I do not see us getting a significantly better deal than that because while they might want trade they won't want trade at the cost of EU member states (plus, ya know, we've just blown a load of political goodwill at this point..).
So, as it stands, we'll probably end up paying in about 2 billion a year for 'free trade' with little to no say on the rules.
(I have made that number up, but I reached it by looking at what Norway pays per capita, multiplying by the UK population, then deciding that £7.4 billion was insane (and also what was left once I dissected the rest of our "£350 million a week" figures) and scaled it back massively, so it feels legit to me.)
(The £350 million figure is also fun because, ignoring if that's the true amount or not, the massively implied thing from 'leave' was "lets spend this on the NHS", which was clearly not going to happen because that money is required to pay for the things the EU already pays for.. so we are probably looking at £100 million a week, which would just about plug the NHS gap today, however it won't in 2 years when that money has become available, and that assumes that nothing else comes out of it... on a related note, I'm looking forward to the tax cut which will be paid for from that £100 million/week...)
