If Brexit takes place, a number of alternative arrangements are possible - see Alternatives to membership: possible models for the UK outside the EU - (a document required by the Referendum Act 2015 and issued by the government).
For example, the "Norway model" is discussed in Chapter 3. It is noted that the Norway model "has considerable access to the Single Market but not in agriculture and fisheries. It does not give access to the EU’s trade deals with countries outside the EU and still requires customs checks on goods crossing into the EU. It also involves making a significant contribution to EU spending, accepting free movement of people, and taking on EU rules without having a vote on them."
In Brexit- Referendum - A few points (20th February) I asked whether the referendum bound the government in law. Constitutionally, since sovereignty rests with Parliament, the referendum result cannot be legally binding on Parliament but, politically, it would be very difficult for the government to ignore the referendum result and I do not see any reason to suppose that the result would be ignored.
What the referendum itself does not address is what would be the UK's relationship with the EU after the UK leaves. Essentially, under the Treaty on European Union Article 50, there is a basic 2 year period for negotiating the terms on which the EU leaves - the process is outlined in Brexit- Referendum - A few points and UK and the EU (6) -Will Brexit be a simple process?
There is a lack of clarity about what Article 50 actually requires. It tells us that there is to be an agreement "setting out the arrangements for withdrawal" but the contents of such an agreement are not specified. It may be that the Article 50 agreement does not need to cover all matters and there will be numerous areas to be addressed. In particular, any UK-EU trading relationship may take many years to establish. Then there are many other areas such as criminal justice - e.g. the European Arrest Warrant. If not dealt with by the Article 50 agreement, such topics would have to be dealt with by separate UK-EU treaties.
Ultimately, Parliament will have to legislate for whatever arrangement comes about. It is said that the legislative process will be very complex and lengthy and the form of any legislation will naturally depend on what arrangements will exist post-Brexit.
Matters could become even messier if, for example, there is a Remain majority in (say) Scotland but not in England. That could fuel demands for Scotland to secede from the United Kingdom.
A general election?
Could a Brexit vote could trigger a General Election. The Prime Minister and most Ministers have campaigned for Remain so how would they stand if the vote is for Brexit?
Since the Fixed-term Parliaments Act 2011 it is not possible for the Prime Minister to simply ask The Queen to dissolve Parliament. The next election will be in May 2020 unless a general election is called because one of the procedures in section 2 of the Act is applied. These are basically - (1) that the House of Commons votes for an early election (note the two-thirds requirement) or (2) that there is a successful motion of no confidence in the government and that is not reversed within 14 days. Parliament cannot be otherwise dissolved.
Given that Parliament has legislative supremacy it could of course repeal the 2011 Act and provide for an election and for new election arrangements for the future. On this, see the interesting post on the UK Constitutional Law blog - Prerogative Powers and the Fixed-term Parliaments Act.*
Whilst the 2011 Act was passed for the benefit of the 2010-15 coalition government, it now appears to suit the incumbent government.
At this stage it is difficult to foresee a situation in which a general election might arise before 2020 but a week may be a long time in politics and several months or even years are very much longer!
* A. Horne and R. Kelly, ‘Prerogative Powers and the Fixed-term Parliaments Act’ UK Const. L. Blog (19th November 2014) (available at http://ukconstitutionallaw.org)
20th February - Brexit ~ referendum ~ a few points - including link to the deal secured by the Prime Minister
UK and the EU (1) - History and Background
UK and the EU (2) - The EU Treaties - key points
UK and the EU (3) - The Parliament, the Commission and the Court
UK and the EU (4) - Freedom of movement of persons
UK and the EU (5) - Referendum - People need facts not slogans (Lord King)
UK and the EU (6) -Will Brexit be a simple process?
UK and the EU (7) -Your Rights
UK and the EU (8) - Trading bloc or emergent State
UK and the EU (9) - A monumental referendum - information to assist