How would leaving the EU affect Sovereignty, & therefore the UKs' constitution?

How would leaving the EU affect Sovereignty, & therefore the U Ks' constitution?

Since the 'rise (and fall) of UKIP', ( which is also the title of another banterous blog-post i did like ages ago) the issue of the EU has been tense. Following 2015, the torys included in their manifesto to hold a referendum on the issue, which was predicted for 2017.
However, its been confirmed to be held on June 23th this year. One of the main reasons to leave the EU is that Britain will become sovereign again or will it?
Sovereignty is said to lie in the EU, as it has ultimate power. Although a fair amount of power does lie in Parliament, which allows laws to be made, if laws passed via Parliament conflicted with the EU, it would override Parliament.
Therefore, in theory, if the UK left the EU full sovereignty would return to Parliament..right?
Michael Fallon, the Defense Secretary, stated that the idea that Britain can be fully sovereign and self governing outside the European Union is "an illusion".
He also states that “Of course there are those who would like Britain to have – not simply the illusion, but the fact – of being a self-governing nation again, where our parliament and courts are absolutely supreme again,”
'“But the difficulty is this – if we got back to the ‘golden age’ where our parliament is absolutely sovereign, you would still have the European Union next door, taking decisions that affect our trade and businesses and our way of life.”
(Quotes from here ) 

A principle of the Uks constitution is EU Membership - but obviously if the referendum is accepted, this would have to change. This states 3 things - 
1) European Law is higher than statute law. This was first established in the Factorame case in 1991, when the European Court of Justice suppressed certain parts of the Merchant Shipping Act 1988 because they conflicted with the Treaty of Rome.If the UK left the EU, it would have no higher law to abide to, So, in theory, Parliament would have no restrictions, not even being binded by its successors. 

2) Some EU bodies, notably the European Commission, have supranational powers. 
This allows for EU bodies to impose their will on member states, being able to disregard their personal stance taken by national legislatures.
Again, if the UK left the EU, this wouldn't be able to happen. Pretty simple, really. 

3) The decline of the 'national veto'. The national veto has been seen to protect the presence of sovereignty in Parliament, by allowing any members to block European courts/ European Union measures that threatened the vital national interest, 
(Last time saying this i promise) So, if the UK left the EU, this national veto would not be necessary as EU measures would no longer apply to the UK.

In general, if the UK was to leave the EU, Sovereignty wouldn't really return to the UK and the principles of the constitution would have to be altered quite a bit.