How Would Leaving the European Union Affect Sovereignty and Therefore the UK's Constitution?

How would leaving the European Union affect sovereignty and therefore 

the UK's Constitution?

It was recently announced by Prime Minister David Cameron that a referendum regarding the UK's place within the European Union is to be held on the 23rd of June, the decision to leave or stay could have serious long and short term repercussions for the United Kingdom. All British citizens over the age of 18 will be able to take part in the nation-wide referendum, its still being debated whether there will be a large turnout or not. I personally see staying within the EU as a beneficial thing, it makes the UK more influential world wide , as well as aids the economy. Never the less many of those promoting Britain's exit from the EU seem to claim that the UK will become sovereign once again, is this really the case? If so will this affect our constitution? 

According to the constitution Britain's sovereignty lies within the Houses of Parliament, its this political institution that holds the power to create laws, put in place laws or remove them completely. However since the UK became part of the EU it has in fact lost some of its sovereignty, for example all EU laws now completely over shadow laws put in place by our parliament, additionally the European Convention of Human Rights can intervene in certain issues and may stop the passing of a 'British Bill of Rights'. Admittedly a lot of our sovereignty has been taken from Westminster and is now transferred to Brussels. If we were to leave the European Union we would no longed be obliged to align ourselves with EU laws and conventions, it would give the country greater power when it came to dealing with holding suspected terrorists or deporting immigrants, at the cost of security and economic factors.

The un-codified constitution of the UK will also be affected if we leave the European Union, to begin with the UK could now introduce a wide variety of new Bills as they're no longer under EU regulations. Furthermore various statutes and conventions concerning trade and so fourth with the EU can now be over looked as its no longer binding, this could have a negative or a positive affect on the economy.

Overall if the UK did decide to opt out of the European Union it would receive the majority of its sovereignty back, however as Defence Secretary Michael Fallon stated 'The Golden Age' of sovereignty is over and the EU is still going to be able to influence the UK even if it leaves the EU. Never the less Westminster would see a boost in its power, at the cost of throwing Britain into the unknown.