Is the UK freer to negotiate trade deals?

The "out" campaigners have told the British population that they are free to negotiate trade deals with more countries; however, is this true? Trade agreement has to be mutual beneficial; therefore, both sides of any trade deal tend to be equally treated and receive the same trade deals. There won't be any unfair trade agreement for the UK to take advantage of. Preferential trade agreement is being negotiated between the EU and countries like the US, Japan and some African and South American countries. A stand-alone investment agreement is being negotiated between the EU and China. With all preferential trade agreements in place and being negotiated, all the super economies have trade agreements with the EU besides China. Britain can negotiate a deeper trade deal with China, the second largest economy in the world and Britain can also hope to get a better deal with the US independently. Moreover, Britain can negotiate trade deals with the Commonwealth countries. All of these targets are correct and doable; however, I think that the only better deal that the UK can get outside the EU is the deal with China, as there is no trade deal being negotiated between the EU and China. When negotiating trade deals with other countries, the British economy is not as large as the EU economy, which gives Britain a weaker position and when Britain in the EU, Britain has influence on the EU trade negotiations with other countries. Therefore, Britain is less likely to get better trade deals when Britain leaves the EU. Moreover, the two developed countries in the Commonwealth countries are New Zealand and Australia, which are potential free trade partners of the EU. The best trade deal Britain can get from its Commonwealth countries is the free trade deal and free trade deals with the two wealthy Commonwealth countries can be done without the UK leaving the EU. To conclude, when Britain leaves the EU, Britain can increase its trade with China; however, the trade deals between Britain and other countries is unlikely to be more generous than when Britain is in the EU.