Does the 2016 Brexit referendum show a clear result?

I don't think the referendum result is a clear and unequivocal one. The EU leave achieved approximately 52% in its favor, mere 2% above the neutral 50%. Admittedly, the difference between 48% and 52% is 4% rather than 2%. However, the 2% data point is justified to be selected as the relevant one given that it would suffice to change the minds in the opposite direction of slightly more than these 2% of people for the result of the referendum to be the opposite.

Exit from the EU seems to be a change of constitution-changing character and therefore, constitution-changing supermajority should be required for that to happen. However, in the UK, there does not seem to exist a special supermajority threshold required to make changes to the constitution; in fact, there does not seem to be any single document entitled "Constitution". Furthermore, supermajority was not required for Sweden when it joined the EU with mere 52.3% gained in a referendum in favor of joining the EU.

Am I right? Is there in fact a supermajority threshold in the UK? How do the judges in the UK know which bills are parts of the implied constitution and which bills are not?

Percentages achieved in referendums for EU entry, from Wikipedia:
- Austria: 66.6%
- Croatia: 66.67%
- Czech Rep.: 77.3%
- Denmark: 63.3%
- Finland: 56.9%
- Hungary: 83.8%
- Ireland: 69.9%, 68.7%
- Italy: 88.1%
- Latvia: 67.5%
- Lithuania: 91.1%
- Malta: 53.6%
- Norway: 47.8%
- Slovakia: 93.7%
- Slovenia: 89.61%
- Sweden: 52.3%
- U.K: 67% - 1975
Of the above, Finland's, Malta's and Sweden's percentages are suspectly low; Norway percentage did not lead to EU entry. Denmark's 63.3% is below 2/3 but above 60%, which is the threshold required in the Czech Republic to change its constitution.

A haphasard selection of constitution-changing parliamentary majorities is as follows, based on WP:
- Austria: 2/3
- Australia: 50% in the house, but referendum has to succeed as well, with two kinds of majorities required for the referendum, one per vote and one per state
- Czech Republic: 3/5
- France: 50% in a referendum, or 3/5 in Congress
- Germany: 2/3 except for immutable areas of constitution
- Ireland: 50% in a referendum
- Italy: complicated, with 2/3 figuring there in some way, but with the alternative option of referendum, it seems
- U.S: 2/3 in the houses, or something more complicated in relation to national convention
- Slovakia: 3/5
- South Africa: 2/3

Some relevant links:
- Why was the Brexit referendum conducted as a simple majority vote?, stackexchange.com
- Parliamentary sovereignty, parliament.uk
- Category:Referendums related to European Union accession, wikipedia.org
- United Kingdom European Communities membership referendum, 1975, wikipedia.org
- Constitutional amendment, wikipedia.org
- Template:Constitutions of Europe, wikipedia.org
- Referendums related to the European Union, wikipedia.org