I do not know of any school of though or author that approached the problem from the same angle you did (representativeness timeline in between decision and implementation of a referendum). However the problem is known. This is the reason why doing a referendum is actually a multiple stage process.
How the issue of representativeness is dealt with in Referendums (EURA 2015)
Let's analyze specifically the one you've mentioned: European Union
Referendum Act 2015 (EURA2015, i.e. Brexit Referendum). The EURA2015 is what is known as a Consultative Referendum. This implies that the referendum is non-binding (it does not automatically translate to law or implementation):
(emphasis is mine)
... [EURA2015] is a type of referendum known as pre-legislative or
consultative, which enables the electorate to voice an opinion which
then influences the Government in its policy decisions. The
referendums held in Scotland, Wales and Northern Ireland in 1997 and
1998 are examples of this type, where opinion was tested before
legislation was introduced. The UK does not have constitutional
provisions which would require the results of a referendum to be
implemented, unlike, for example, the Republic of Ireland, where the
circumstances in which a binding referendum should be held are set out
in its constitution.
This means that it is the government and parliament role to ensure that the Referendum decision has proper representativeness at the time of implementation (or decision) and decide whether to go forth or not with the decision.
A strict interpretation of the rules seems to show that the current government/parliament does approve of the representativeness of the Referendum result and agrees with it (although this is a complex subject in itself). The issue you've mentioned is being dealt with (in theory) at this stage.
Precedents for contentious results in Referendums
You did not ask this but the reported association of the leave field with Post Truth Politics has been dealt with extensively both in media and academia. The circumstances were quite different but this situation is not without precedent (other referendums regarding the EU have had negative responses in other countries). This is the case Denmark (Maastricht Treaty) and Ireland (Nice and Lisbon Treaty) where two referendums where made with a negative response in the first and a positive in the second.
"The answer lies in the specific dynamics of referendum campaigns. In
a referendum, the typical No campaign strategy aimed at rejecting the
treaty on offer is to associate the proposal with unpopular themes and
thereby drive down public support for it. The No campaigners therefore
have a structural advantage, as they need only to raise doubts in the
minds of voters. This state of play, however, typically only holds for
the first referendum held on a treaty, not for the second."
(Atikcan, 2015; see also The Puzzle of Double Referendums in the European Union)
"Voters in a referendum obtain information and derive voting cues
from a variety of sources. Some of these, such as political parties or
ideological orientations, are similar to those also found to be
influential in elections. Others can be quite different. In some
referendums, the issue may be entirely new and unfamiliar to many
voters, initiating a ‘learning’ or ‘cue–taking’ process specific to
the campaign itself. In referendum campaigns, parties may be
internally divided and sometimes send conflicting signals to their
electorates. As a result, voting behaviour in referendums often
exhibits greater volatility than is found in elections." (Leduc,
Alternative models for Referendums
There are some academics that have proposed some differences or alternatives to the current models. An example is Tsebelis " Veto Players " or Referendums that take into account the notion of Willingness_to_pay (Haab, et al, 1997). In some referendums the multiple choice model is used providing greater flexibility in voting (like in an election).