As I understand it in the EU we could only trade within ourselves. Ie only within the European market.
Not true - just go an have a look at your clothes labels and see where they were made - then look at your TV and car.
By leaving, we'd surely be broadening our options and be able to trade freely with any country we wanted (obviously dependent on whether they wanted to trade with us) as opposed to only those we were told we could trade with?
Trading and trading freely are totally different things. At the moment you don't have to pay a tax to export to the EU or to import from it, how we trade depends on the agreement with individual countries outside the EU and after Brexit whatever we can negotiate with the EU.
How can that be construed as a bad thing?
Because at the moment we have free trade with the EU, we don't need to negotiate or pay taxes.
So say you are building a car in the UK but the engine is built in Germany, at the moment you just import he engines for the cars, put them in the car and sell them to the EU.
No import of export tax.
Now if the EU decides we have to pay 10% on all imports form the EU the cost of cars of making those cars is going to go up, therefore the price to sell will go up. In addition people may well not want to buy a car made outside the EU.